Heading into the 2007 Major League Baseball Draft, Beavan was considered a top prospect, with the ability to throw his fastball at consistently, and as fast as. The Texas Rangers selected Beavan in the first round, with the seventeenth overall selection. He was one of three high school pitchers chosen by the Rangers in the first round of the draft. Beavan signed with the Rangers, foregoing college, for a signing bonus of $1.5 million. In his first professional season, Beavan had a 10–6 record and a 2.37 ERA in 23 games started for the Clinton LumberKings of the Class-A Midwest League. By 2009, Beavan pitched for the Bakersfield Blaze of the Class-A Advanced California League. He was promoted to the Frisco RoughRiders of the Class-AA Texas League in June 2009. In 2010, Beavan had a 10–5 record and a 2.78 ERA in 17 games started at for Frisco, where he was named the Rangers' Minor League Pitcher of the Month for May. He received a promotion to the Oklahoma City RedHawks of the Class-AAAPacific Coast League.
Seattle Mariners
Soon after the promotion, on July 9, 2010, Beavan was traded to the Seattle Mariners along with Justin Smoak and fellow prospects Matt Lawson and Josh Lueke for Cliff Lee and Mark Lowe. The Mariners assigned Beavan to the West Tenn Diamond Jaxx of the Class-AA Southern League. Beavan started the 2011 season with the Tacoma Rainers of the Class-AAA PCL. He pitched to a 5–3 record and a 4.45 ERA with Tacoma. On July 2, 2011, the Mariners announced that Beavan would be making his big league debut on July 3 against the San Diego Padres. The Seattle Mariners beat the Padres 3–1 with Beavan going 7 innings and giving up 1 earned run on 3 hits. Beavan entered the 2012 season in contention for a spot in the Mariners' starting rotation. He won a spot in the rotation for Opening Day. Beavan threw a quality start opposing Philip Humber during Humber's perfect game on April 21, 2012. On August 2, 2014, the Mariners outrighted Beavan off of the 40-man roster.
Beavan threw five pitches. His primary pitch was a four-seam fastball at 90–93 mph, and he had a two-seam fastball with similar velocity that was used frequently against left-handed hitters. His main off-speed pitch was a curveball in the mid-to-upper 70s, although he also threw a changeup to lefties and a slider to righties.
Personal life / Post playing career
Beavan is the youngest of three children. His elder brothers are 13 and 11 years older than him. Both of his brothers played college baseball, but neither played professionally. Beavan's wife, Allison, is a cyclist. The two rode together in an effort to help Beavan lose weight during the 2011–12 offseason. As of 2019, Beaven was a youth baseball coach for Dallas Tigers WEST.