The area between middle and lower reaches of the Yangtze River is the largest region for soft wheat production in China. In soft wheat breeding, the lack of germplasm with desirable quality for end-use products is a barrier. Ningmai9 is the main variety of soft wheat planted in this area. To create germplasm with better quality and yield potential than Ningmai9, mutants of HMW-GSs in Ningmai9 induced by ethylmethanesulfonate (EMS) were obtained. SDS-PAGE showed that two mutants, md10 and md11, were HMW-GS 1Dy deletions. DNA sequencing confirmed that one mutation was caused by a C/T substitution, resulting in the change of CAA encoding glutamine into the termination codon TAA, and another mutation was due to a G/A substitution in the central repetitive domain of the coding region, causing TGG encoding tryptophan to become the termination codon TGA. The premature termination codon of the 1Dy12 gene affected the expression of 1Dy12 and kept the mRNA at a lower transcription level during the kernel development stage in comparison with the wild type. HMW-GS 1Dy12 deletion mutants decreased the content of HMW-GSs and glutenin macropolymers, mixograph envelope peak time and TIMEX width, water solvent retention capacity (WSRC), and lactic acid solvent retention capacity (LASRC). In the HMW-GS 1Dy12 deletion lines, the sugar-snap cookie diameter was 8.70–8.74 cm, which was significantly larger than that in the wild type of 8.0 cm. There were no significant differences in spike number, kernel number, thousand kernel weight, and yield between the deletion lines and wild type. Overall, the study indicated that the knockout of the HMW-GS gene induced by EMS is an effective way to improve wheat quality, and deletion mutants of HMW-GS 1Dy12 decrease gluten strength and increase sugar snap cookie diameter without yield penalty in Ningmai9 wheat.