Biodegradable polyesters are excellent candidates for sustainable packaging and mulch films. Poly(butylene succinate terephthalate) (PBST) and poly(glycolic acid) (PGA) possess excellent barrier properties and specific mechanical properties. Herein, reactive melt-blending of PGA and poly(butylene adipate-co-terephthalate) (PBAT) using a multifunctional epoxy oligomer (ADR) and diphenylmethane diisocyanate (MDI) was conducted to improve their mechanical performance and processability. With increasing content of the compatibilizer, the cross-sectional microstructure showed a decreased phase size and blurred interface, which effectively improved the interfacial adhesion and compatibility. Compared to PBST/PGA blend films without compatibilizers, the tensile strength increased from 32.8 to 39.4 or 47.2 MPa after addition of 0.1 ADR or 0.5 MDI. The tear strength increased from 146.2 to 162.1 or 174.1 N/mm. Meanwhile, the compatibilized PBST/PGA films showed stable barrier properties and maintained their mechanical properties when subjected to an ultraviolet light accelerated aging test. Finally, a field trial was carried out using the blown PBST/PGA mulch films spanning nearly four months to assess their processability for practical application. Thus, this work promotes a sustainable PBST/PGA film with excellent strength and barrier properties, made via a reactive melt-blending method, that shows great potential as an agricultural mulch film.