WELCOME to LMF...
You are right about it not being good for the battery... but that is not going to be a big problem...
A bigger risk is running the PTO clutch with low voltage, It can start to slip as you get below 10 volts or so...
That will eventually burn up the clutch.
So don't run it till the battery is completely dead.
Check fuses, wiring and connectors... You could have a voltage regulator gone bad....
With a little caution you should be able to continue mowing until you get around to fixing the charging problem. :smile:KennyV