There were 3 meanings for the prefix be-. (1) on all sides, besmear, or thoroughly, bestir. (2) much or to excess, beclamor/becrush/bedew. (3) Privative, off or away, behead/bereave/beshear

Oxford English Dictionary: Forming derivative verbs with privative meaning ‘off, away,’ as in bedeal v., benim v., bereave v. A very common use of be- in Old English and Middle English, prob. originating in words like beshear v., ‘to cut all round,’ whence ‘to cut off or away’; but no longer in living use in forming new derivatives.