On SOA (Sons of Anarchy), a "mayhem vote" is when the charter votes to decide whether to kill a member or not.
The vote takes place during "church", a congregation of the entire charter used to make important decisions and discuss matters that affect the club.
Any decision made at church requires a vote. Usually, majority wins - but in the case of the mayhem vote, it must be unanimous.
As far as I can remember, the only person that get's voted on in this way is Clay Morrow.
The first time, he survives the Mayhem Vote because Bobby votes against it.
The second time, even though Clay is technically no longer a member of SAMCRO, a mayhem vote takes place nonetheless, and it's unanimous.
Clay is shot dead alongside members of the IRA towards the end of Season 6.