Deaf signers with damage to their left hemispheres suffer from forms of sign aphasia (a loss of the ability to produce and/or comprehend language ) that are virtually identical to the aphasia of hearing victims with similar lesions. (They) are unimpaired at nonlinguistic tasks that place similar demands on the eyes and hands, such as gesturing, pantomiming, recognizing faces, and copying designs. Injuries to the right hemisphere of deaf signers produce the opposite pattern: they remain flawless at signing but have difficulty performing spatial tasks, just like hearing patients with injured right hemispheres.
It is a fascinating discovery. The right hemisphere is known to specialize in (spatial) abilities, so one might have expected that sign language, which depends on (spatial) abilities, would be computed in the right hemisphere. (But) language.. is controlled by the left hemisphere. The left hemisphere must be handling the abstract rules and trees underlying language, the grammar and the dictionary and the anatomy of words, and not merely the sounds and the mouthings at the surface.
From The Language Instinct by Steven Pinker