A 2004 graduate of Lamar High School, Savery was a four-year starter and letterman for the Lamar Redskins. During his tenure at Lamar, he earned first team all-state and first team all-greater Houston. He was a three-time first team all-district 18-5a honoree, and was voted the most valuable player in the district in 2004. Joe was named the 2004 Proline player of the year after hitting .556 with 7 home runs and 40 RBI as a senior. He also went 11–0 on the mound with 93 strikeouts, posting a 0.53 ERA. Joe lead the Redskins to be nationally ranked in 3 different polls during his senior year.