Is "mast" in "beech mast" related to the same syllable in "masticate"?
Not that I can find, but there's a funny missing link. The first is an old word of steady meaning in middle and old English, Dutch, High German, back to an OAryan root for 'to be fat, to flow', cf. Sanskrit for 'fat'. The second is from Spanish and French words which may come from the Greek word for jaw. But between those, in the OED, are a couple of mast* headwords having to do with the breast, as "mastalgia", from the Greek word for breast.
I can leap from 'fat & flowing' to 'breast' easily. I don't know enough Greek to guess if their 'breast' and 'jaw' actually are related. The first is rendered μαστος, the second μασταξ, if I'm reading the tiny characters correctly. (There should be a mark like an acute accent over the ο in the first word, but I don't see how to represent that in HTML entities.)
Or, from :
I think that I shall never see
A poem lovely as a tree.
A tree whose hungry mouth is prest
Against the sweet earth's flowing breast;
And when the pigs come eat their fill
I guess it's all mast for the grill.