Mystery card workaround

When I'm playing a mystery card set and my player is performing in a way that indicates he got his worst card, if I drop him and pick him back up does it reshuffle the deck and give him another randomly generated card? Same for a player that gets dropped by another team?

NO you will get the same card back----the cards are determined when each league is created, and stay the same for that league through the season.

If you know you have a poor card (an injury can tell you) dump him for someone else, especially if the drops are still 5%, sometimes you just have to go with your instincts if a card is doing poorly.