Excessive cadmium (GrCdc) and deficiencies of copper (GrCuc) and magnesium (GrMgc) in grains pose serious human health risks. Common wheat breeding has reduced the genetic diversity within elite germplasm resources, negatively impacting future wheat production. Thus, identifying loci controlling GrCdc, GrCuc, and GrMgc in tetraploid wheat and introducing them into common wheat is essential for genetic improvement. In this study, we identified quantitative trait loci (QTLs) for GrCdc, GrCuc, and GrMgc using the Wheat 55K single nucleotide polymorphism (SNP) array-based linkage map and phenotypic data across multiple environments in recombinant inbred lines derived from a cross between a wild emmer accession (LM001) and an endemic tetraploid wheat in Sichuan, China (Ailanmai). Four major stably expressed QTLs were identified, three of which (QGrCdc.sau-AM-5A for GrCdc, QGrCuc.sau-AM-4A for GrCuc, and QGrMgc.sau-AM-4A for GrMgc) were novel. These loci were validated using tightly linked kompetitive allele specific PCR (KASP) markers in various genetic backgrounds. Several candidate genes with sequence variations (TRIDC5AG052690, TRIDC5BG060070, and TRIDC4AG008520) were predicted to influence Cd, Cu, or Mg absorption and transport within these QTL intervals. Correlation analysis revealed that GrCdc was not correlated with GrCuc or GrMgc, although GrCuc was significantly correlated with GrMgc. Furthermore, no significant effects of GrCdc, GrCuc, or GrMgc on agronomic traits were detected, as no correlations between them and any of the 11 agronomic traits investigated were observed. In addition, QGrCuc.sau-AM-4A colocalized with QGrMgc.sau-AM-4A, suggesting potentially shared physiological and/or genetic control. Altogether, these stably expressed QTLs across environments provide theoretical guidance for further germplasm improvement and fine mapping.