Dissociate and its synonymous sibling disassociate can each mean "to separate from association or union with another." Both trace back to the Latin verb sociare, meaning "to join," which comes in turn from socius, a noun meaning "companion." (Socius is associated with many English words, including social and society.) Dis- in this case means "do the opposite of," so both dissociate and disassociate indicate severing that which is united.