Thanks Reed. Been racking my silly brain on how to do this, and it was right there in front of me all along.

So BorgPokerPro, go to Game > Game Settings > League Settings > Functions > Reset Functions (left side of page) and hit one of the bottom three options "Erase MLB career stats...", "Erase all Career Stats...", or "Erase the entire league history".
I would go with one of the stats options myself because you don't want to wipe out service time, which I think is what erasing the entire league history would do.