The copolyester poly(butylene glycol adipate-co-terephthalate/diphenylsilanediol adipate-co-terephthalate) (PBDAT) was synthesized by the melt polycondensation method using terephthalic acid, adipic acid, 1,4-butanediol, and diphenylsilylene glycol as the raw materials. The molecular chain structure, thermal properties, thermal stability, mechanical properties, and degradation behaviors of the copolyesters were investigated. The results showed that the prepared PBDAT copolyesters exhibited good thermal stability and mechanical properties. With the increase in diphenylsilanediol (DPSD) content, the thermal stability of PBDAT and the melting temperature both increased. The tensile strength and elastic modulus of PBDAT also exhibited an increasing tend. When the DPSD content was 12.5% (PBDAT-12.5), the tensile strength, the elastic modulus, and elongation at break were 30.56 MPa, 238 MPa, and 219%, respectively. With the increase in diphenylsilanediol content, the hydrophilicity of PBDAT decreased, but PBDAT still shows good degradability and the thermal degradation T5% temperature was 355 °C. The thermal degradation of PBDAT was also improved.