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This sense development arose in the consequence of the wars waged by Otto the Great and his successors against the Slavs, a great number of whom they took captive and sold into slavery. [Klein]

Meaning “one who has lost the power of resistance to some habit or vice” is from 1550s. Applied to devices from 1904, especially those which are controlled by others (compare slave jib in sailing, similarly of locomotives, flash bulbs, amplifiers). Slave-driver is attested from 1807; extended sense of “cruel or exacting task-master” is by 1854. Slave state in U.S. history is from 1812. Slave-trade is attested from 1734.

Old English Wealh “Briton” also began to be used in the sense of “serf, slave” c.850; and Sanskrit dasa-, which can mean “slave,” apparently is connected to dasyu- “pre-Aryan inhabitant of India.” Grose’s dictionary (1785) has under Negroe “A black-a-moor; figuratively used for a slave,” without regard to race. More common Old English words for slave were þeow (related to þeowian “to serve”) and þræl (see thrall). The Slavic words for “slave” (Russian rab, Serbo-Croatian rob, Old Church Slavonic rabu) are from Old Slavic *orbu, from the PIE root *orbh- (also source of orphan), the ground sense of which seems to be “thing that changes allegiance” (in the case of the slave, from himself to his master). The Slavic word is also the source of robot.