A pair of migrant thugs who attacked two of New York’s Finest are back on the street after Manhattan prosecutors agreed to cut them loose without bail, The Post has learned.

Brian Joseph, 24, and Jose Gonzalez, 19, were both arrested Sunday after scuffling with cops on traffic patrol on Eighth Avenue shortly after 9:50 p.m. — allegedly biting one officer and hurling a moped at the other, according to law enforcement sources and officials.