The anionic ring-opening polymerizations (AROP) of bio-based N-acetyl homocysteine thiolactone (NHTL) and different epoxides were carried out using benzyl alcohol and 2-tert-butylimino-2-diethylamino-1,3-dimethylperhydro-1,3,2-diazaphosphorine (BEMP) as initiating system. This polymerization is a rare example of AROP in the presence of an acidic moiety (acetamido group). Well-defined alternating poly(ester-alt-sulfide)s are obtained with number-average molar masses Mn ranging from 1.7 to 13.0 kg mol−1 and dispersities as low as 1.14. The presence of one acetamido function in the lateral group on each repeating unit of the copolymers derived from NHTL results in very significant increases (up to 94 °C) of the glass transition temperature Tg compared to similar poly(ester-alt-sulfide) derived from petro-based γ-butyrothiolactone (BTL). These functional poly(NHTL-alt-epoxide)s are valuable structures with numerous potential applications due to the presence in each repeating unit of one cleavable ester group and one redox-sensitive thioether group.