We have developed an efficient diastereo- and enantioselective Mannich/cyclization cascade reaction of α-substituted isocyanoacetates with 4-aryl-3-carbonyl-1,2,5-thiadiazole-1,1-dioxide type cyclic sulfamide ketimines cooperatively catalyzed by cinchona alkaloid-derived squaramide and AgOAc. The corresponding optically active 2,3,3a,4-tetrahydroimidazo[1,5-b][1,2,5]thiadiazole-1,1-dioxide derivatives were obtained in excellent yields (up to 99%) and good to excellent stereoselectivities (up to >20 : 1 dr, up to 94% ee).