The present study aimed to determine the influence of organic amendments (OAs) on neutralizing the harmful effect of copper (Cu) on black mustard (Sinapis nigra L.). In a pot experiment, three levels of copper pollution were used: 200, 400, and 600 mg Cu kg−1, against a control without Cu. The soil was amended with three types of OAs: pine bark (PB), peat moss (PM), and cattle manure (CM). Our research showed that plant condition depends on the Cu content in the soil. Increasing soil contamination significantly affected the plant yield, leaf greenness index, and dry matter content. The type of OA had no significant effect on the condition of black mustard (BM); however, each had a different effect on neutralizing the harmful effects of Cu. CM reduced Cu accumulation, PM showed no effect, while PB contributed to a significant increase in Cu content in BM plants. The chemical composition of BM depended on the Cu content in the soil. With increased soil contamination with Cu, the contents of Ntot, K, Mg, Ca, and Na in BM increased, while the content of P decreased. In terms of mitigating the harmful effects, CM was more beneficial than PM and PB. Among the analyzed OAs, CM, and PM contributed to Cu immobilization, while PB promoted Cu mobilization in contaminated soils.