Yes, CLUTCHES is a Scrabble word!

Letter values in Scrabble US: C 3, L 1, U 1, T 1, C 3, H 4, E 1, S 1.

Is it a valid word?

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

the act of grasping
the act of grasping
a tense critical situation
a number of birds hatched at the same time
a collection of things or persons to be handled together
a woman's strapless purse that is carried in the hand
a pedal or lever that engages or disengages a rotating shaft and a driving mechanism
a coupling that connects or disconnects driving and driven parts of a driving mechanism

Also: clutch bag, clutch pedal, cling to, hold close, hold tight, get hold of.

Not playable in Scrabble US: PREHEND.