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The wielder's Attack stat cannot be lowered. Does not block self-inflicted Attack drops, such as the Attack drop from Superpower. It also does not block the effects of Haze, Heart Swap, or Power Swap.
Hyper Cutter is a great ability for any physical attacking Pokemon that wants an immunity from having its precious Attack being dropped, which could potentially be the difference between a successful sweep and an abysmal failure. However, its use is exceedingly situational, as Intimidate is not as popular as it used to be, so the residual Attack drops are not as common as they were in past generations. What's more, no Pokemon outside of Xatu and Prankster Murkrow uses Attack-lowering moves such as Growl and FeatherDance intentionally, and instead favor the Attack-lowering side effect of burns, which Hyper Cutter does not bypass. Still, Kingler makes use of it, since Shell Armor is even more situational and not as useful.
Found in Dream World