Various well-defined diblock copolymers with poly(alpha-methylene beta-butyrolactone) (PM beta BL) segment were prepared by salen aluminum complexes or aminoalkoxybis(phenolate)yttrium amido complex mediated living ring-opening polymerization of racemic alpha-methylene-beta-butyrolactone (rac-M beta BL) and different lactones via one-pot, two-step method. These diblock copolymers all consist of semicrystalline and amorphous segments, possessing both a melting point and a glass transition temperature. With the use of simple salenAlMe with bulky (tert-butyldimethylsilyl) groups on the phenolate ortho position as catalyst in conjunction with equivalent benzyl alcohol, M beta BL and beta-butyrolactone (BL) have nearly identical reactivity in their copolymerization, affording the copolymers P(M beta BL-ran-BL) with random distributions of the two monomers. Notably, these copolymers exhibited tunable degradability in the presence of Lewis base, dependent on the M beta BL unit content in the random copolymers. Moreover, the vinylidene groups in P(M(beta)BLzran-BL) copolymers could be further functionalized through radical initiated cross-linking reactions and thiol-ene click chemistry, producing functionalized and cross-linking polymers with enhanced thermal property. These strategies will provide enormous possibilities to synthesize diverse well-defined block and random copolymers with designable segments or functional groups.