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I have owned a MTD Pro Z2560 for about 4 years, and it has never failed me before. A few days ago, I started it, and drove it around for a while. After 10 minutes I noticed that it was beginning to slow down. Not enough to affect performance, but enough for me to notice it. Then I started to drive down a hill, and was unable to stop it's downward momentum enough to avoid smashing into a tree at what felt like about 20 MPH. Luckily, I was able to pull the parking brake in time. Half an hour later, I tried backing it up the hill again, and failed, driving almost uncontrollably down the hill. I tested the problem going forwards as well, and it seemed to work slightly better. (Admittedly, the results may have been skewed, as I got more room to accelerate going forwards.)

My guess is that there is something wrong with the motor's strength, but I really don't know anything about lawnmowers, or how to actually troubleshoot them. Thanks in advance for any help.

First thing to do is use your eyes.
Get under with a nice strong light .
Look at the control arms left & right should be a mirror image of each other.
Follow the linkages all the way back to the controls on the motors.
Look for leaking oil on the wheel motor &/or Pump if it has one.
Check the oil level in the drive reseviour ( if it has one )
Check both of the wheel motor bypass valves

Unfortunately, the drive system is hydrostatic which is directly bolted to a geared axle assembly. These units are serviceable but are a pain to work on. the relationship between the hydro and axle is a fickle pair and if serviced the two must be aligned perfectly.
the symptom you are describing is typical of a hydro unit that is failing. First do what Bert said, look for signs of leakage etc and linkage. however, if it worked fine for 15-20 minutes or so, then slowed down, it is a hydro issue.
what happens in the inside of the unit is that there is a piston block assembly on both the input and output side. where this block assy rides against the center section it can get scored. it starts as minor scoring and the oil acts as a sealant to seal the two together. however, as the scoring gets worse, the oil will seal when it is cool as it is thicker. as the unit warms, the oil thins and will actually "leak" between the block and center section. this leak is internal and cannot be seen from the outside.
i have searched for a parts list for the hydro unit but cannot find one right now however, i may have a different source if needed. a complete unit is about $1000.
below is list for the complete mower.

parts list for the mower - https://www.partstree.com/parts/mtd...mmz-2560-53ab5b8j195-mtd-pro-zero-turn-mower/

If both drives are doing the same thing at the same time I would say replace your belt.