When you pop an engorged tick, does it die?
Yep. Next question!!
What would you expect it to do? be visited by a little tick medic, have its guts rammed back inside, and continue a normal life?
One of the problems is that the engorged abdomen of the tick can be burst without immediately killing the tick. Insects are tenacious survivors and the head of the tick can remain alive for some time after the initial trauma.
This may result in nasty secondary infections due to the head further burying itself in the host. For this reason it is always important to remove the entire parasite. The traditional methods of burning or unscrewing are best.
See this threadfor a lively discussion on the best tick removal method. Burning is not a good idea