In　this　paper,　we　develop　a　unified　dynamic　intelligent　reflecting　surface　(IRS)　beamforming　framework　to　boost　the　sum　computation　rate　of　an　IRS-aided　mobile　edge　computing　(MEC)　system,　where　each　device　follows　a　binary　offloading　policy.　Specifically,　the　task　of　each　device　has　to　be　either　executed　locally　or　offloaded　to　MEC　servers　as　a　whole　with　the　aid　of　given　number　of　IRS　beamforming　vectors　available.　By　flexibly　controlling　the　number　of　times　for　IRS　reconfiguring　phase-shifts,　the　system　can　achieve　a　balance　between　the　performance　and　associated　signalling　overhead.　We　aim　to　maximize　the　sum　computation　rate　by　jointly　optimizing　the　computational　mode　selection　for　each　device,　offloading　time　allocation,　and　IRS　beamforming　vectors　across　time.　Since　the　resulting　optimization　problem　is　non-convex　and　NP-hard,　there　are　generally　no　standard　methods　to　solve　it　optimally.　To　tackle　this　problem,　we　first　propose　a　penalty-based　successive　convex　approximation　algorithm,　where　all　the　associated　variables　in　the　inner-layer　iterations　are　optimized　simultaneously　and　the　obtained　solution　is　guaranteed　to　be　locally　optimal.　Then,　we　further　derive　the　offloading　activation　condition　for　each　device　by　deeply　exploiting　the　intrinsic　structure　of　the　original　optimization　problem.　According　to　the　offloading　activation　condition,　a　low-complexity　algorithm　based　on　the　successive　refinement　method　is　proposed　to　obtain　high-quality　suboptimal　solutions,　which　are　more　appealing　for　practical　systems　with　a　large　number　of　devices　and　IRS　elements.　Moreover,　the　optimal　condition　for　the　proposed　low-complexity　algorithm　is　revealed.　The　effectiveness　of　the　proposed　algorithms　is　demonstrated　through　numerical　examples.　In　addition,　the　results　illustrate　the　practical　significance　of　the　IRS　in　MEC　systems　for　achieving　coverage　extension　and　supporting　multiple　energy-limited　devices　for　task　offloading,　and　also　unveil　the　fundamental　performance-cost　tradeoff　embedded　in　the　proposed　dynamic　IRS　beamforming　framework.