Saxon attended Arcardia High School, where he played as a wide receiver, defensive back and punter.
After graduation he moved on to Pasadena City College, punting for the 1980 Metropolitan Conference champion.
He lost his job after struggling with his production, but regained it in the tenth game of the season against Brigham Young University, setting a school record with an 80-yard punt.
On August 27, he was waived after averaging 43.5-yards per game during the preseason and the team deciding to keep incumbent Mike Black.
In the 1970s and early 1980s the Dallas Cowboys had the luxury that they didn't need to carry a punter on their roster, because quarterback Danny White could perform that role at a high level.
In order to avoid a potential injury to White, the team kept searching for a replacement until finding Saxon.
In 1987, he established himself as one of the best directional punters in the NFL, by leading the league for a second consecutive season with 20 punts inside the opponent's 20-yard line.
In a total of 6 career postseason contests, he averaged 43.5 yards, ranking third in NFL playoff history.
On July 7, 1993, he was released after the team decided to have a training camp battle with young punters, which was won by John Jett.
[7] He averaged 42.4 yards per punt and was named AFC special teams player for week 6, after his game against the Phoenix Cardinals.