And then there's the saw as a saying (from MW):

Main Entry: 4saw
Function: noun
Etymology: Middle English sawe, from Old English sagu discourse; akin to Old High German & Old Norse saga tale, Old English secgan to say -- more at SAY
Date: before 12th century
: MAXIM, PROVERB

That in mind (maxim, proverb), apply this meaning to Geoff's:

holesaw, the whipsaw, the sabre saw, the hacksaw, scroll saw, rip saw, crosscut saw, and maybe even the see saw... and Father Steve's coping saw and fretsaw.