Does the body still get rid of sperm in the body if your on the depo provera shot? or does it hold it there and the sperm live until you stop taking the shot? and therefore being possible to become pregnant after having the shot discontinued?

Sperm are released from the male with limited energy reserves. They will die off after using up all their energy in ~5 days in the best environment. The die off sooner if stressed by air drying or other external stressors. They are not capable of hanging around for weeks/months waiting to get you pregnant.

Sperm has a short life once ejaculated. Five days is the outer limit for viability and you can not get pregnant from sperm after that interval. Depo provera would not affect the survival of sperm.