I am not sure of the style of hydro you may have in this JD but the only
disc (on the out side) I know of on your standard lawn and garden tractors
that are a hydro trans is a brake disc which unless it is binding and
putting excess load on your unit wont be the problem. Start by changing the
fluid (and filter if it has one) as contaminated fluid and or low fluid will
give you poor performance and possibly effect how it operates. Also make
sure the outer case of the trans is not all packed up with grass and or dirt
causing the unit to over heat, if there is a fan (I can't remember seeing
one without a fan of some sort) see if it is broken or missing also causing
it to over heat.
If changing the fluid don't work and the belts and linkages are fine and it
is not overheating then you can either attempt to repair it and take apart
the pump and or trans axle but I do not recommend this. Only attempt this if
you have the proper work place that is relatively dirt free to prevent
contamination when reassemble, the knowledge and the technical spec's to do
the job. The second choice which I would recommend is take it to a shop.
If the pump is damaged it will loose power as the oil in the hydro get hot
and becomes thinner, the hot oil can bypass through the damaged part more
easily instead of the pump and provide the power to the wheels. You could
call the local JD shop and see if they have some tips you can try for your
particular unit. Make sure you have any model number they may need to help
you when you call.