Sounds to me like the charging system is NOT working properly. The PTO is an electromagnent, and draws a ton of current in order to stay engaged. Chances are, if you drove the tractor around long enough without the PTO engaged, it would drain the battery too, just take a lot longer. When your tractor is running at wide open throttle, you should see about 14 to 16 volts at the battery terminals. If not, then the charging system is not working. If it's reading less than 14 volts, even 13 volts, it's bad. Most likely its the voltage regulator that is bad, and it is an easy fix, two screws and 3 spade connectors, and you're off to the races.
Here is a copy of the wiring diagram. You can ignore my notes, as I was trying to test the PTO switch when I copied this originally.