Improved utilization of rice (Oryza sativa L.) straw and Chinese milk vetch (Astragalus sinicus L., vetch) has positive effects on rice production. So far, few studies have investigated the productivity of vetch under different residue management practices in double-rice cropping system. The effects of rice straw on the growth and nutrient accumulation of vetch across seven years (2011–2017) and the subsequent effects of rice straw and vetch on two succeeding rice crops in a vetch–rice–rice cropping system, with the vetch established by relay cropping, were examined. The seven-year double-rice experiment consisted of the following treatments: (1) 100% chemical fertilizer (F-F100); (2) only vetch without chemical fertilizer (M-Con); (3) 80% chemical fertilizer plus vetch plus a low-cutting height (low-retained stubble) with the removal of straw (M-F80); (4) 80% chemical fertilizer plus vetch plus a low-cutting height with the retention of straw (M-F80-LR); (5) 80% chemical fertilizer plus vetch plus a high-cutting height (high-retained stubble) with the retention of straw (M-F80-HR); and (6) no fertilizer (F-Con). The yields of the two rice crops after vetch were not affected by either the cutting height of stubble with retention of straw or by the management of straw (retention vs. removal) with low-cutting height of stubble. The yields of the two rice crops after vetch were significantly higher for M-F80-HR than for M-F80-LR, but the relative contributions of the high-cutting height and straw retention to the higher rice yield could not be determined in this study. The yield stability of the double-rice grain in M-F80-HR was also increased, as determined by a sustainable yield index. Significant increases in vetch biomass and nutrient uptake were observed in the fertilized treatments during the rice season compared with the unfertilized treatments. In M-F80-HR plots, improvements in the growing environment of the vetch by conserving soil water content were associated with the highest vetch biomass, nutrient uptake, and yield stability of vetch biomass. These increased nutrient inputs partially replaced the demand for chemical fertilizer and stimulated the rice yields. It can be concluded that retaining higher-cutting stubble residues with straw retention could be the best straw management practice for increasing the vetch biomass and nutrient use efficiency, thereby allowing utilization of high-cutting height with retention of straw and vetch to improve the stability of rice productivity in a double-rice cropping system.