I received your pictures and see why you thought it might be Mark Twain's signature. It does bear quite a strong resemblance to Sam Clemens' written signature. I've attached a link to a very good Twain site with samples of variations on Clemens' signature in case you haven't seen it.
http://etext.virginia.edu/railton/sc.../yrstruly.html
I'll give you my opinion, for what it's worth, and a couple of other places you might want to contact.
First of all, the painting itself looks to me to be later in style and execution , that is, mid-twentieth century or later. It has the look of a study from a painting class - that sort of thing. I'm certainly not an expert in those matters so you might want to get someone from a museum or gallery to give you an opinion on that.
Second, I find no evidence as yet that Clemens ever spent the kind of time studying or practicing that would have allowed him to produce this sort of work. You might want to check out his essay, "Instructions in Art" where he talks about his own art work and illustrates the piece with drawings. As is often the case with Clemens, the essay is tongue in cheek and the drawings are humorous. They are however, typical of anything I've ever seen in terms of Clemens drawing. This essay appears in "Complete Humorous Tales and Sketches of Mark Twain" edited by Charles Neider and also in "Mark Twain Himself" by Milton Meltzer which you should be able to find at a local library. If you can't, let me know and I'll send you a copy of the essay.
Third, it was uncomon for Clemens to sign himself as "S.Clemens" without the "L", but as you'll see from the web page, there are a lot of variations to his signature. I haven't done a close comparison but at first glance yours looks a lot like that of Samuel Clemens the writer.
Clemens did have a third cousin, Cyril who maintained an extensive Twain collection for many years and also had a son, Samuel who was born in 1939. If your painting is not by Samuel Langhorne Clemens - and I find it quite unlikely that it is - it may be the case that it was done by this Samuel Clemens, the son of Cyril. Cyril lived in the mid-West and Samuel would have been about the right age to have been painting in this style unless I miss my guess so there may be a connection to Mark Twain in that way. I haven't found any evidence of that as yet either, but it might help account for the similarities in the signature.
It may also be that it's just some painter named Clemens - but, as you were perceptive enough to note, the signature is very much like that of Samuel Clemens (Mark Twain) so it seems there's something going on here.
Lastly, I think you ought to get another opinion or two. You might want to send your attachments to Vic Fischer at the Mark Twain papers in Berkeley and see what he might be able to add. In the meantime I'll see what else I can find.