What does offensive Calm Mind do better than MixKrow?
I'm assuming your set is Eviolite, Life Orb, and Timid with the moveset Calm Mind/Roost/Dark Pulse/Heat Wave/Hidden Power Grass/Hidden Power Flying. Such a moveset isn't even possible, but since you haven't specified I'll just account for every option.
With CM, a lot of murkrow's usual counters like chinchou, porygon, magnemite are easily beaten and it also makes a really great misdreavus counter provided they don't carry t-bolt (and even then you can still win if SR isn't up and you win the speed-tie).
Chinchou with Thunderbolt defeats any Murkrow set regardless. A Thunderbolt when you're at +2 followed by a Thunderbolt at +3 will still KO you regardless. Using Roost doesn't really help either, as you're still dead after Stealth Rock. Even if you spin, Chinchou can simply keep Thunderbolting until it gets paralysis, at which point you lose. A +1 HP Grass doesn't always KO 0/0 Eviolite Chinchou. MixKrow, on the other hand, will take out Chinchou with HP Grass + Sucker Punch.
Porygon will not be OHKOed even ny a +2 Dark Pulse, and OHKOes back with Ice Beam even if you're at +2. MixKrow, on the other hand, has a shot at a 2HKO with Brave Bird (and will almost always get it with Stealth Rock), and actually does a better job at beating Porygon because Porygon will not have Prankster Recover.
Magnemite dies, but it dies to Heat Wave from MixKrow anyways.
Both sets defeat Misdreavus anyways and lose to Thunderbolt Misdreavus. MixKrow is more afraid of Will-O-Wisp, but it revenges better with Sucker Punch.
While you can't check as many things as you could previously with sucker punch, you can sweep much more effectively.
I don't think you're going to get Calm Minds on any Pokemon in the metagame. Standard Murkrow checks (Porygon, Chinchou, etc.) do just as well against your set anyways. Also, Sucker Punch is ridiculously good on Murkrow.
I think it's worthy of its own set, especially seeing as you have stuff like parafusion murkrow up there (though, admittedly, it's quite debatable if it should be up).
Parafusion Murkrow is a niche but actually a good set. Offensive Calm Mind, on the other hand, is not.