Adjusting biomaterial degradation profiles to match tissue regeneration is a challenging issue. Herein, biodegradable hyperbranched poly(β-amino ester)s (HP-PBAEs) were designed and synthesized via "A2 + B4" Michael addition polymerization, and displayed fast gelation with thiolated hyaluronic acid (HA-SH) via a "click" thiol-ene reaction. HP-PBAE/HA-SH hydrogels showed tunable degradation profiles both in vitro and in vivo using diamines with different alkyl chain lengths and poly(ethylene glycol) diacrylates with varied PEG spacers. The hydrogels with optimized degradation profiles encapsulating ADSCs were used as injectable hydrogels to treat two different types of humanized excisional wounds - acute wounds with faster healing rates and diabetic wounds with slower healing and neo-tissue formation. The fast-degrading hydrogel showed accelerated wound closure in acute wounds, while the slow-degrading hydrogel showed better wound healing for diabetic wounds. The results demonstrate that the new HP-PBAE-based hydrogel in combination with ADSCs can be used as a well-controlled biodegradable skin substitute, which demonstrates a promising approach in the treatment of various types of skin wounds.