If you sacrifice Mayhem Devil, its ability triggers.

If a permanent is sacrificed to pay a cost of a spell or ability, Mayhem Devil's ability will resolve before that spell or ability. Conversely, if a permanent is sacrificed during the resolution of a spell or ability, that spell or ability will finish resolving before Mayhem Devil's ability is put onto the stack.

A legendary permanent that is put into a graveyard because of the "legend rule" isn't sacrificed.

Mayhem Devil itself doesn't allow any player to sacrifice any permanents. Its ability triggers whenever a player sacrifices a permanent because some other spell, ability, or cost instructed the player to do so.

You control Mayhem Devil's triggered ability and choose the target, no matter who sacrificed the permanent.