You for sure can! Were I doing this I’d use a 3D stitch for the teeth/gums/lips and the outlines of the eye and lower jaw (probably also combined with stitching over layers of felt (or similar) to really bulk up the depth for the whole piece, especially for the horns), but it’s going to be miserable to do and I really don’t expect such coarse stitching to look right when done that way.

The big issue I see is that the shading is just too gentle - most complex embroidery like this looks “cel shaded” because you can’t get smooth gradients with thread, and swapping different colors of thread to produce that look ruins the stitch pattern.

There are a handful of techniques wherein you create the stitch using a single thread on a blank piece, paint the color gradients on with dye, unravel the whole embroidery then recreate it exactly on the final piece. (I own an edo period tapestry where this was done, though it’s faded to where it’s extremely difficult to tell.) Needless to say it’s incredibly rare for anyone to take the time to do it this way anymore

My embroidery machine is really old, like 30+ yrs, with very basic programmability, and it can do stitches in multiple directions. It has a foot plate thing that moves the cloth as needed, and it works pretty well.

I have to imagine a newer more advanced one would be capable of something like this, tho would probably need to be simplified somewhat.