I think my LawnBoy/Toro Pacer can do this; but are we talking of a slope or a mountain-side ?The Honda Commercial mowers will do it. I've also had pretty good luck with my cub cadet, 5-speed self-propelled with the Kawasaki engine. They are available used in the $200.00 range. If money isn't an issue, take a look at the Ventrac mowers. They'll do a 30* slope up and down, and across!
Pacer = push to go, works great, but will not scale a mountain-side..$200 range ?? This LB was around $400; IMO, $200 buys junk.
I'll check out Ventrax.