Aiming at the problem that polydimethylsiloxane (PDMS) and other polymer materials cannot be machined by abrasive air jet at normal temperature, an idea of machining PDMS and other polymer materials by cryogenic abrasive air jet is put forward. A cryogenic abrasive air jet machining device is designed. Cryogenic abrasive air jet at different temperatures can be obtained by changing the length of serpentine tube immersed in liquid nitrogen. A mathematical model for calculating the length of serpentine tube is established, and the feasibility of the model is verified through experiments, which provides a solid foundation for further research on cryogenic abrasive air jet machining. PDMS are machined by abrasive air jet at different temperatures and it is found that abrasive air jet machining for PDMS targets is impossible at room temperature while cryogenic abrasive air jet machining allows the drilling of holes. The cross section qualities of holes machined at low temperature can be improved. The material removal mechanism of cryogenic abrasive air jet machining of PDMS is the combination of ductile erosive and brittle erosive systems.