Since you’ve only had it for a while, my guess is that you’re mistaking the digital clipping at the track output for the distortion function. The signal distorts when you crank the overdrive up, yes, but it’s due to both the distortion effect AND the track level clipping at the output, so you need to turn the track level down to avoid the harshness.
It happened to me, too, at first. I’ve noticed that on the Cycles, you have to be more careful with levels than with e.g. the Digitakt. (I’ve only used the Digitakt, but I assume it might be similar to the Digitone in this respect.) There’s not as much headroom.
I made a comparison with a long bass note with lots of distortion (and track level set to low) and with no distortion, and the difference visible on the Ableton scope is that there’s really nice high harmonics there, so the sound is a lot fatter. Definitely no clipping whatsoever.