Sometimes your only options might be to kill yourself on a turret, monster or minion. How long from the last time an enemy attacked you until you die does it have to be for it not to count towards your enemy score? I belive it is called an execution when you do this.
If a champion dies and hasn't been damaged or debuffed by another champion in the last 10 seconds, it is an execution. Otherwise, the kill is awarded to the enemy champion who last dealt damage.
Executions are generally caused by a turret, minion, or monster. An execution offers no gold but still gives experience to nearby champions on the opposite team.
Also from the Wiki like 2 inches further down.
So basically, if you exhaust an enemy champion at 9 seconds after the damage you dealt it gets reset. The only way for them to dive a tower or minion wave and commit suicide is if it has been 10 seconds since any enemy has inflicted any kind of debuf or damage.
Short Answer 10 seconds;
I Could not find a link to Mocking Shout, so here is the skill description:
Source "A kill is the act of decreasing another champion's health to zero while it has no abilities to prevent death. The last player to strike the target champion is awarded with the kill, and all contributors within the last 10 seconds are awarded with an assist."