Go to the top of the highest hill you have.
Uncouple the trailer then open the bypass valve
If the mower sits there without moving then the hydros are in excellent condition
Try it in both pointing up & pointing down.
If it races away like Mulga Bill's bicycle then the tranny is shot and needs replacing
If it sits there, give it a bit of a push
If it rolls down the hill slowly and occasionally slows down then the tranny is a bit worn.
If the tranny is good using this test then your problem is the drive belt , a pulley in the drive system or a spring as already suggested .
If the tranny is suspect try replacing the oil
JD use tinnner oil than other makers so you can some times squeeze a few extra season out of it by changing the tranny oil to 20w 50