The Giants began the reconstruction of their 31st-ranked defense yesterday by jettisoning veteran linebacker Michael Boley. Though the move saved Big Blue $4.5 million under the salary cap, it appeared to be a matter of performance as much as money after Boley — at times very productive — struggled to stay healthy throughout his four-year stint in New York. The former Falcon, who had landed a five-year, $25 million deal as a prized free agent in 2009, appeared in all 16 games last season, but was barely used down the stretch as the Giants stumbled and followed their Super Bowl triumph by missing the playoffs. “Michael came in and learned our defense quickly, and he added speed — coupled with big-play ability — to our defensive unit,” Giants general manager Jerry Reese said in a statement. “I wish him well as he moves forward in his career.” Boley was set to earn $4.25 million this year, making the eight-year NFL veteran an easy target with the Giants struggling to get under the projected cap for 2013. Third-year pros Jacquian Williams and Spencer Paysinger are expected to contend for Boley’s vacancy at weak-side linebacker this fall. Boley’s release and Osi Umenyiora qualifying for unrestricted free agency are just the start, though. More cuts and paycuts are sure to follow for the Giants. Among the candidates for at least a restructuring is defensive tackle Chris Canty, who is due $6 million. Boley had a career-high three interceptions and two fumble recoveries last season, but he was considered a more important contributor to their Super Bowl-winning team in 2011. Boley, 30, had three fumble recoveries (including one for a touchdown) and also forced a fumble that season, then capped his performance by leading the Giants with 10 tackles in their Super Bowl XLVI win over the Patriots.