Slaughter was born in Stockton, California, where he attended Franklin High School. Upon graduating, he attended San Joaquin Delta College and San Diego State University prior to his professional football career. Cleveland Browns general manager Ernie Accorsi drafted Slaughter in the 2nd round (43rd overall) of the 1986 NFL Draft, based on the strong recommendation of the Browns' Hall of Fame receiver Paul Warfield, who was an unofficial scout for the team in 1986. During his rookie season he was listed at 6'0" and 175lbs, and played in all sixteen games. As a Cleveland Brown, Slaughter would catch 305 passes and 27 touchdowns in six seasons, earning the praise of Accorsi who stated "(He was) one of the best receivers the Browns ever had.
Webster continued his career with the Houston Oilers, the Kansas City Chiefs, the New York Jets and finally with the San Diego Chargers. He was selected to the NFL Pro Bowl in 1989 and 1993. In 1989, while playing with the Cleveland Browns, he averaged 19 yards per reception and a season total of 1236 yards (a franchise record that would stand until Braylon Edwards broke it in 2007 with 1289 yards) and 6 touchdowns. Slaughter finished his career with 563 receptions for 8,111 yards and 44 touchdowns, along with 9 carries for 50 yards.