With the rapid development of electronic skin, smart robots, etc., the past few years have witnessed explosive growth in the number of flexible sensors, and the resulting environmental contamination will be a great challenge. Herein, we propose a strategy to synthesize a polyurethane elastomer with good self-healing and controlled degradation properties for a flexible and stretchable strain sensor. First, polycaprolactone diol (PCL) and isophorone diisocyanate (IPDI) were used as monomers to synthesize the isocyanate-terminated prepolymer and further reacted with adipic dihydrazide (ADH) to obtain a polyurethane elastomer with hierarchical hydrogen bonds. By the prestretching method, a stretchable strain sensor was fabricated with carbon nanotubes as a conductive substance. The obtained elastomer exhibited high tensile strength (16.28 MPa), large stretchability (660%), superior crack tolerance, high self-healing efficiency (92.1%), and special controlled degradability (4 h in 0.5 mol/L NaOH solution). The sensor showed high sensitivity (GF = 111.4), fast response/recovery time (161/180 ms), and good repeatability (3000 stretching−releasing cycles) and was successfully applied for monitoring minute human movements. The strategy to prepare high-performance, self-healing and environmentally friendly elastomers in this work is of great significance for the sustainable development of flexible electronic devices.