What is the etymology of "dewclaw"?
I'm afraid that no one knows for sure. The word is some four hundred years old. Dictionary.com maintains that it may be related to the kind of dew that appears overnight, but it cannot fortify the claim.
Etymonline says:
also dew-claw, 1570s, from claw, but the signification of the first element is obscure (see dewlap).
Dewlap is further down in the same entry:
mid-14c., dewe lappe, from lappe "loose piece" (O.E. læppa), first element of unknown origin or meaning. Originally of cattle.
Dictionary.com is virtually identical on dewclaw (it refers to dewlap too), but there is a little more in its origin entry on dewlap:
1350–1400; Middle English dew(e)lappe, apparently dewe dew + lappe lap1; compare Danish dog-læp, Dutch (dial.) dauw-zwengel; literal sense is unclear
YourDictionary.com cites American Heritage Dictionary, 4th Ed. for a claim that "dew" may be an alteration of "toe", but it also says prob. so called because it does not touch the ground, but only the dew on the surface.
Dog or dew may be cognate with Scots dewg/Old Scots duig, always used in the plural and having the meaning "small pieces, shreds, fragments" (see Dictionary of the Scots Language), suggesting "fragmentary claw". This connection was proposed in a thread on the subject at The Straight Dope.
The OED says
Apparently < dew n. + claw n. (Perhaps referring to the fact that while the other claws come in contact with the soil, or press the grass to the ground, this only brushes the dewy surface.)