The aim of this research was to determine the effect of sex, castration, and processing on the chemical properties of mutton in the production of kaštradina—a traditional Dalmatian dry-cured meat product. Therefore, the carcasses of 20 ewes (E), 20 rams (R), and 20 wethers (W) of the Dalmatian pramenka breed were processed by dry-curing. On the 1st, 35th, and 60th days of processing, the samples from the scapulae were taken, then the proximate chemical, NaCl, and mineral analyses were performed, and significant differences between most of the parameters were found. Unlike W, the R samples contained significantly more proteins (p < 0.01), NaCl (p < 0.05), and potassium (p < 0.05) and less fat (p < 0.05). Furthermore, compared to the W and R categories, the E category of kaštradina contained significantly more calcium (p < 0.05). The higher contents of intramuscular fat, potassium, and calcium and lower content of NaCl could positively affect the sensory (marbling, flavor, juiciness, and tenderness) and chemical (fatty acid profile) properties of kaštradina. These findings suggest that the W and E raw mutton could be a better-quality raw material for production of kaštradina than could the R, but further research is needed for a more comprehensive picture of its quality.