There are going to be some people that say any slope is too much. Then there are going to be some that say don't worry about it because they have no problem mowing the drainage ditch out by the road.
Here's the thing: The front wheels caster. They don't have any positive steering - or in most cases braking - control whatsoever. So mowing sideways across a slope will cause the mower to turn in the direction of the slope. Imagine pushing a shopping cart across a slope. It will attempt to turn downhill. That's the effect I'm talking about.
Now if the slope is mild, that downhill steering tendency is easily countered by slightly altering your control inputs. It's no big deal and you quickly learn to just correct for it keep on mowing. But when the slope gets steeper, it becomes a chore at best.
Now let's consider a more dangerous scenario. Steep enough that you actually slide. The amount of slope needed to slide is of course variable. What kind of tires do you have? Is the grass wet with dew? Are you using abrupt control inputs? Anyway if you start sliding out of control most zero-turn mowers don't have much in the way of ability to regain control except to just wait until you've reached a spot with less slope. And the last place you want that stopping point to be is in your creek.
I'm not going to tell you what to use for your mowing duties. Just wanted to paint a picture of what the zero turn mowers are - and are not - capable of.
xtn