Despite the extensively researched physical principles, numerous published simulations on SiC drift step recovery diodes (SiC DSRD) and the practical implementation of SiC DSRD-based pulses, there are few kinds of research focusing on collaborative design between a SiC DSRD and its driving circuit. In this paper, a collaborative design method of a SiC DSRD and its driving circuit are presented. In addition, a detailed simulation is conducted to verify design considerations and to analyze the impact of driving parameter changes on the output pulse waveform. A pulse generator prototype with a self-developed SiC DSRD is implemented. The experimental results show that the circuit can output a peak voltage of 790 V on a matching load of 50 Ω, with a rise time of 520 ps (20%~80%), and can work at a 1 MHz repetition frequency rate with good stability.