Either the pump or the valve chest.
They are both repairable.
You would be best served bu contacting Tuf Torq and finding your local service agent.
usually they will want the tranny only.
It looks like the pump is a bolt on item at the front of the tranny.
In hydraulic terms the unit is a cheap piston pump one.
In mower terms it is very expensive.
There is a fairly complicated air bleed to be done in any case.
Tuff Torq have repair manuals that they will generally send you, but you have to ask them, nicely.
If not I have a copy I can send you if you PM me. Fairly sure TT sent it to me.
If you go to simplicity and type in your model & serial number you can download the parts book & perhaps the full service manual.
In any case the parts book has a hydraulic schematic diagram so at least you can work out where it all fits.
If you do take it apart make sure you mark the input & return lines and take a lot of photos.
Plug all oil lines ( test tube stoppers work really well for this )
There is a lot of hours in this job so getting it done will not be cheap, and the pump itself is a very high precision item and precision costs money.
Mulligans have also been very good to me in the pasts and have been really good to a lot of people who the list has referred to them.
They know their stuff & will give you good advise about what your options are regarding repairs.
And whatever happens please get back to the list with the outcome.
That will greatly help others in your position.