45 degrees is a sure bet you will flip. I used my backhoe to make the grandkids a show hill. At the top it measures 45 degrees. I had to clear the top 20 ft by hand, take sand and gravel and dump it over the hill to level out by hand. It's hard to walk on a 45 degree angle. Try walking on a roof with 12-12 pitch, that's 45 degree.
The bottom of the hill I had to put the back bucket down and use it as a safety device to keep from flipping over. Only guessing, but the bottom of the hill is between 25 and 30 degree.
I wouldn't even want to attempt to mow a 25 degree hill safely.
People who mow ditches with a chopper will usually get the chopper wet, if not killed. Everytime I see one in the ditch, I want to take a pic and post it.
If I had to mow a ditch, I would rig up a pipe to extend over the ditch bank, use chains to drag a mower. Propably make the mower from an old 4-6 ft belly mower, put wheels on it and put a 20-25 hp vertical shaft motor on it.
If you don't want someone taking a pic of you, don't do what I saw someone do to mow a very steep hill.
This person used a push mower, attached it to a 20 ft ladder. The other end of the ladder was attached to the front of an ATV. He used the ATV to push the mower up the hill. George