Self‐healable degradable networks encounter a growing popularity for biomedical applications due to their ability to recover their properties after damage. Self‐healable hydrogels dominate with applications in tissue engineering and drug delivery. On the opposite and despite their potential for medical devices, self‐healable elastomers remain scarce, especially if they must be compatible with fused deposition modeling (FDM) 3D‐printing and self‐heal at physiological temperature under a hydrated state. These unmet challenges are addressed in this work with degradable elastomeric networks based on dynamic imine bonds prepared from multi(aldehyde) and multi(amine) hydrophobic PEG‐PLA star‐shaped copolymers. The star topology of these copolymers is the key feature of the strategy as it allows the design of multifunctional high molecular weights pre‐polymers that ensure an efficient dynamic chemical crosslinking while guaranteeing access to the FDM process generally restricted to thermoplastics. The proposed elastomeric networks combine high self‐healing efficiencies at 37 °C (>97%) with mechanical properties compatible with soft tissues and a linear degradation profile. Their FDM processing to produce self‐healable tubular devices is demonstrated. Finally, their cytocompatibility is assessed and confirm their potential as biodegradable elastomeric networks to be used for the design of self‐healable 3D‐printed devices for biomedical applications.