The 5-foot-10 Harris was a second-round pick in 2011 and played in 16 games last season, recording a career-high 20 tackles and four passes defensed. Groves, a second-round pick in 2008, has career totals of 157 tackles and 8 1/2 sacks for four teams.
The Texans also cut Chris Boswell, who was competing with Randy Bullock for kicking duties. Among the other cuts were receiver Travis Labhart, defensive end Keith Browner, linebacker Max Bullough, tight end Anthony Denham, nose tackle Ricardo Matthews, receiver Uzoma Nwachukwu, fullback Toben Opurum, tight end Zach Potter, safety Jawanza Starling, defensive end Julius Warmsley, cornerback Marcus Williams and linebacker Chris Young.
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