Yes, CLEAVERS is a Scrabble word!

Letter values in Scrabble US: C 3, L 1, E 1, A 1, V 4, E 1, R 1, S 1.

Is it a valid word?

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

annual having the stem beset with curved prickles; North America and Europe and Asia
a butcher's knife having a large square blade

Also: goose grass, spring cleavers, galium aparine, meat cleaver.

Not playable in Scrabble US: CATCHWEED.