Living copolymerization of mixed monomers can enrich the diversity of copolymer materials with well-defined performance via controlling both monomers and stereosequences. However, periodic sequence-controlled living copolymerization of same-type monomers with more than two components in synthetic polymer science remains a challenge. In this work, a new method of monomer-promoting asymmetric kinetic resolution-alternating copolymerization can let a tricomponent mixture of l-lactide (S,S-LA or l-LA) and two enantiomeric isomers of racemic tropic acid cyclic esters (tropicolactone) be polymerized into sequence-controlled -(ASASBS)n- type biodegradable copolyesters (the subscript S presents the configuration and A and B present lactic acid units and tropic acid units, respectively), and diblock copolymers of -(ASASBS)n-b-(ARARBR)n- can further be obtained upon addition of R,R-LA (d-LA). Compared to previous asymmetric kinetic resolutions of racemic chemicals via polymerization or organic reactions, no enantiopure catalyst/initiator is required in this system. After the resolution and alternating copolymerization of S,S-LA and rac-tropicolactone, the ee value of unreacted tropicolactone can reach 99.4%. The alternating probability between tropicolactone and lactide monomers is more than 96% in periodic sequence polymers of -(ASASBS)n-. The tetracomponent mixture of rac-lactide and rac-tropicolactone can be copolymerized into an alternating copolymer with a -((ASASBS)x-ran-(ARARBR)y)n- structure, in which the stereoselective linkage probability of 95% after S,S-lactide (R,R-lactide) followed by S-tropicolactone (R-tropicolactone) keeps very high too.