Saber-Tooth vs. Ground Sloth
Now that we've met both the Saber-Tooth and the Giant Ground Sloth, we can see how an artist's rendition shows how they may have interacted with the saber-tooth going for the neck of this giant beast.
Unfortunately, I don't think the artist took too close a consideration of the size proportions of the fingers of the sloth. Otherwise, this may have been how things went down in the past.