Yes, SAWYER is a Scrabble word!

Letter values in Scrabble US: S 1, A 1, W 4, Y 4, E 1, R 1.

Is it a valid word?

SAWYER is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

one who is employed to saw wood
any of several beetles whose larvae bore holes in dead or dying trees especially conifers

Also: sawyer beetle.