Alexis attended and played basketball at Christ The King Regional High School, in Middle Village, Queens, New York.

Alexis played college basketball for the Syracuse Orangemen, from 1982 until 1986, being a starter during his senior year and earning All Big East Conference honors.

Alexis was drafted by the Golden State Warriors, just one pick ahead of future Hall of Fame member Dražen Petrović.

From 1988 until 1993, Alexis played in Italy, where he reached the domestic championship's finals in 1989, as a team member of Enichem Livorno.

Alexis spent another year in Italy, at Reggio Calabria, before joining French club Levallois.