A Mexican immigrant walking home from work was savagely beaten on Staten Island in a hate crime, cops said yesterday. Alejandro Galindo, 52, was on Forest and Jewett avenues in Elm Park around 12:10 a.m. Thursday when he was approached by three unidentified African-American men who started shouting anti-Mexican slurs, law enforcement officials said. The thugs started attacking Galindo, who managed to escape.