I thought you could sample anyone in a mixtape, because you are realeasing it for free. Ive been listening to Jon Connor's mixtape and he samples everyone from Kings of Leon, Cyndi Lauper and even Aldous Snow (Fictional band in Forgetting Sarah Marshall) and there is no way he got permission for any of them.
Just like you can cover any song live without permission as you are not individually obtaining money for that song, you should be able to sample on a mixtape.
Actually, the bar/venue/restaurant is (or, to be legally safe, should
be) paying for bands that play cover songs by paying for an ASCAP or BMI license.