Catalyzes the aldol cleavage of 4-hydroxy-4-methyl-2-oxoglutarate (HMG) into 2 molecules of pyruvate. Also contains a secondary oxaloacetate (OAA) decarboxylase activity due to the common pyruvate enolate transition state formed following C-C bond cleavage in the retro-aldol and decarboxylation reactions (By similarity). 4-hydroxy-4-methyl-2-oxoglutarate = 2 pyruvate H(+) + oxaloacetate = CO2 + pyruvate Divalent metal cation. Homotrimer. Belongs to the class II aldolase/RraA-like family.