Maybe it's just the art style — the Cheat's baffling physiology probably would make for a pretty horrific-looking creature in a more realistic style — but I don't even see how The Cheat counts as ugly.
In Charlie The Unicorn, there is a strange... sea-goat-seal...thing. Charlie even lampshades this. "I can't tell if you're adorable or creepy."
In Protectors of the Plot Continuum, when a canon character's name is misspelled in badfic, a 'mini' creature appears: a small version of a monster from that canon. For Lord of the Rings, Mini-Balrogs, and for Harry Potter, there are Mini-Aragogs, etc. These are cute, but also just as ugly as their larger counterparts.
Fluffy Pony can be this, especially when abusers want to emphasize the oddity of the creatures.
Hellephant on Regretsy (sadly the site has been shuttered), who inspired some adorable fan art despite still being stained and missing an ear.
As hard as it is to believe, there have been times where SCP-682 could be considered "cute", such as his interaction with the benevolent Blob Monster, SCP-999 or his exposure to rage-inducing Creepy Child, SCP-053.
SCP-191 could also be seen in this light. Although in her case its mostly because people feel sorry for her.
The eponymous creature from the Welcome to Night Vale episode "The Visitor", which Cecil initially fawns over as being straight up adorable. However, his description of it is very...odd, with it being vaguely spherical, with stubbly little nubs for limbs are large, staring 'duck eyes', until even Cecil is forced to admit it might not be cute so much as just plain weird. Of course, after what it does to the station cat, its hard to think of it as cute in any capacity.