I'm really torn on the idea of Mixpert in general. I just don't know what situations the special options of Surf and Ice Beam are clearly better than the physical options of Waterfall and Avalanche. Earthquake is a given, as is, if you're smart, little to no Attack EVs like Misty said. It really comes down to the pokemon that Swampert has anything to do with, and that means both from a countering perspective and what's going to be switching in on Swampert itself. So allow me to go down the threat checklist and try to determine what's really the best option for Swampert; physical or mixed.
First, let's assume:
240HP / 044Atk / 216Def / 008 Spd / 000SpA / 000SpD EVs for
401HP / 267Atk / 297Def / 158 Spd / 187SpA / 216SpD stats, Impish
and
240HP / 000Atk / 216Def / 000 Spd / 052SpA / 000SpD EVs for
401HP / 256Atk / 297Def / 140 Spd / 219SpA / 216SpD stats, Relaxed.
297Def reaches the highest possible magic stat point and is constant for both Impish (+Def, -SpA) and Relaxed (+Def, -Spd), as is 401HP. The Impish one has a decent chance of outspeeding enemy Swampert hence the 8 Spd EVs, but the rest of the (expectedly) few EVs are put into Attack. The Relaxed variant would probably benefit more from putting all of its leftover EVs into SpA, since it has two actual special attacks and the difference between 256Atk and 267Atk is negligable, especially when you reconsider the "purpose" of a Relaxed one and its special attacking capabilities in the first place.
Finally, we can assume EQ/Avalance/Waterfall/filler for Impish and EQ/IB/Surf/filler for Relaxed. That filler's going to be Stone Edge or Protect or actually a filler in Stealth Rock most of the time, but won't really factor in besides on Gyarados and Zapdos, off the top of my head (which is why I'm actually bothering to run through the threat list lol). So here goes.
Tyranitar: Wash, both 2HKO with EQ
Gyarados: Relaxed. This is matchup with possibly the most implications so bear with me. Impish Pert are "more likely" to carry Stone Edge, though HP Electric is an extremely viable option on a Relaxed variant:
Relaxed, 219 SpA Swampert's Hidden Power Electric on a 384HP/236SpD (near-max/min) Gyarados: 50-60%
Relaxed, 219 SpA Swampert's Hidden Power Electric on a 380HP/246SpD (near-max/min) Gyarados: 49-57%
Relaxed, 219 SpA Swampert's Hidden Power Electric on a 332HP/236SpD (4EVs/min) Gyarados: 58-68%
Pretty much always a 2HKO, even on non-bulky versions. Now for the other "filler" in Stone Edge, which both Swampert variants are capable of running:
Relaxed, 256 Atk Swampert's Stone Edge on a 384HP/235Def (near-max/60%) Gyarados: 41-49%
Relaxed, 256 Atk Swampert's Stone Edge on a 380HP/211Def (near-max/25%) Gyarados: 46-55%
Relaxed, 256 Atk Swampert's Stone Edge on a 332HP/194Def (4EVs/min) Gyarados: 58-68%
All percentage ranges are 2% higher from an Impish, 267 Atk Intimidated SE except on 332HP/194 which is 60-71%.
So basically it's clear that accuracy is the issue here (assuming this isn't Wifi where HP Electric is almost out of the question). Stone Edge is pretty much a borderline 2HKO on any bulky variant, however Stealth Rock and Sandstream are factors in Swampert's favor. However, much of this whole issue deals with Intimidate as it pertains to both Gyarados and Salamence, which will very much play out, especially with Bulkier Gyarados.
Relaxed, 256 Atk Swampert's Intimidated Stone Edge on a 384HP/235Def (near-max/60%) Gyarados: 28-33%
Relaxed, 256 Atk Swampert's Intimidated Stone Edge on a 380HP/211Def (near-max/25%) Gyarados: 31-37%
Relaxed, 256 Atk Swampert's Intimidated Stone Edge on a 332HP/194Def (4EVs/min) Gyarados: 39-46%
All percentage ranges are 1% higher from an Impish, 267 Atk Intimidated SE.
So, if Swampert is your best/only Gyarados counter, it would make a lot more sense to run HP Electric as your filler on a therefore Relaxed Swampert for a pretty much guaranteed 2HKO, not Stone Edge and definitely not Protect and Stealth Rock, which Gyarados will happily (angrily?) Taunt. You don't counter pokemon with a 20% of CHing that's equal to your chance of missing...not when Swampert's your best/only Gyarados counter and it can literally be a bit scared by Intimidate if it isn't figuratively by the prospect of countering Gyarados in the first place.
Infernape: Wash, both OHKO with EQ or get owned by Grass Knot
Azelf: Wash. Azelf takes 44-52% from a predicted 219SpA Surf and 45-53% from a predicted 267Atk Waterfall, and while the 60 initial BP of Avalanche will clearly do worse damage than IB, you're not staying in anyway. This is a great example because Azelf's equal Base Def and SpD (70) indicate Waterfall is a very slight favorite over Surf, given what I feel to be, for the reasons stated above, extremely reasonable EV spreads.
Rhyperior: Relaxed. Obviously Surf is better, and Rhyperior is much more likely to invest in Def than SpD anyway. For what it's worth, a 219 SpA Swampert Surf does 95-112% to 434HP/146SpD Rhyperior, while a 267Atk Waterfall does only 58-68% to 434HP/296Def, and both defensive stats are at their respective minimum (assuming max Atk I guess but does it matter lol).
Electivire: Wash, both OHKO with EQ and take the same from HP Grass.
Heracross: Impish. Heracross has 75 Base Def and 95 Base SpD.
Salamence: Relaxed. Much of the reasoning behind this is the same as with Gyarados so I won't reiterate it, but I will say this — Swampert really, really isn't a Salamence counter in DP like it was in Advance.
Togekiss: Impish. Togekiss's 115 Base SpD seal this one...but are you staying in on a Grass Rope capable pokemon with 120 Base Special Attack?
Gengar: Impish. Gengar has 60 Base Def and 75 Base SpD.
Garchomp: Relaxed. A 219 SpA and Garchomp's 359Atk SDed EQ does 68-77%...but it knows it can pretty much SD again if Swampert's switching in on its SD, because what Swampert will have the ~266 SpA necessary to OHKO it with Ice Beam? Avalance does 114-134% from 267 Atk if Swampert takes a hit, and 58-68% if not. A 219 SpA Ice Beam will do 75-88%, meaning if Garchomp's taken any damage it will likely die.
However, you should never, ever switch Swampert into Garchomp unless it's weak as hell and you're at max HP, so Swampert vs. Garchomp should rarely ever play out. I don't like gambling that Garchomp will EQ and give Avalance 120 power though, personally, I just don't think many smart battlers will really think their once SDed EQ will OHKO a max or near-max HP Swampert, and if they do it's because they know they're Adamant and Life Orbed (does 93-109% to 401HP/297Def).
Raikou: Wash, both OHKO with EQ
Lucario: Wash, both OHKO with EQ
Rampardos: Wash, both likely OHKO with EQ
Weavile: Wash, both 2HKO with EQ
Dugtrio: Wash, both OHKO with EQ
Jolteon: Wash, both OHKO with EQ and take the same from HP Grass.
Aerodactyl: Impish, Aero has 65 Base Def and 75 Base SpD
Snorlax: Wash, both EQ or have no business in on Lax without a Roar filler (Curse)
Zapdos: Relaxed. If Zapdos is actually staying in and hitting you with a HP, it's probably Grass and going to do a lot of damage.
Blissey: Wash, both EQ
Sceptile: Relaxed. IB does more on the switch which is obviously the only time Swampert will have anything to do with Sceptile.
Metagross: Wash, both 2HKO with EQ
So...the point of yet another Jumpman Wall of Words? You may be disappointed, but the answer is "it depends on your team", which you don't really need a detailed analysis to have figured out for yourself. Impish is great for Heracross and Togekiss, while Relaxed is great for Rhyperior and Gyarados. But only, in the event of Gyara, if you have HP Electric, which means you're already thinking outside the box and know what your team can and can't handle, which you need to do when deciding on Impish or Relaxed in the first place (, which is why I typed all this lol).
I didn't forget about pokemon like Skarmory or Weezing that Mekkah mentioned, with which Swampert will have to contend even if they aren't technically threats, but I am not sure I care enough about those two to really actually prefer Relaxed to Impish. Weezing owns Swampert every day of the week, especially if it wants to counter Rhyperior with HP Grass and therefore has Swampert covered too. And Skarmory...is 3HKOed by EQ either way with it Feather Rests on a slower STAB EQ user. For what it's worth, 267 Atk does 42.77-50.22% on 334HP/416Def Skarmory (max/max), which means the Relaxed variant can actually better pose the threat of a OHKO with a CH that's more likely every time Skarmory thinks an RBY-esque Recover Loop is a good idea against Swampert.