No bike handles sticky mud well. The fatter the tire, the longer you'll keep moving. I see lots of trashed drivetrains on cyclocross bikes at cyclocross races; it's par for the course.

I rode a cross race on my fat bike (they had a separate fat tire category for fun), and it still was wiggly in spots due to the loose and sticky mud. I don't understand riding a cross bike in such conditions, but there were plenty of folks doing it, grinning through the mud in their teeth.

To be blunt, you should stay off the trails when they're that muddy. If you're picking up that much mud then you're doing damage. Consider that next time, and go around the mud like you said. Both the trail and your bike will be happier.