Wearable electronics have showed their profound impact in military, sports, medical and other fields, but their large-scale applications are still limited due to high manufacturing costs. As an advanced micro-fabrication process, laser processing technology has the advantages of high speed, high flexibility, strong controllability, environmental protection and non-contact in preparing micro-nano structures of wearable electronics. In this paper, a 355 nm ultraviolet laser was used to pattern the copper foil pasted on the flexible substrate, and the interconnection electrodes and wires were constructed. A processing method of multi-parallel line laser cutting and high-speed laser scanning is proposed to separate and assist in peeling off excess copper foil. The process parameters are optimized. A stretchable 3 × 3 light-emitting diode (LED) array was prepared and its performance was tested. The results showed that the LED array can work normally under the conditions of folding, bending and stretching, and the stretch rate can reach more than 50%. A stretchable temperature measurement circuit that can be attached to a curved surface was further fabricated, which proves the feasibility of this process in the fabrication of small-scale flexible wearable electronic devices. Requiring no wet etching or masking process, the proposed process is an efficient, simple and low-cost method for the fabrication of stretchable circuits.