The objective of this work was to modify minimally two agro-industrial wastes, to evaluate their effectiveness for the retention of copper in soils contaminated by mining tailings, as well as to evaluate the changes in the chemical forms of the metal in the soil and thus also evaluate the attenuation of copper desorption in a short period after a mine tailing spill on the soil. The solid wastes of olive mill and grape stalks of the wine-making process were modified minimally, through washing processes and partial alkalization, to obtain substrates with greater capacity for copper sorption. Two agricultural soils near a tailing impoundment were studied: a sandy loam soil with pH close to neutral and high total and available copper content and a clay soil with low copper content, slightly acid pH, and high clay content. Both soils were treated with mine tailings from the same site to simulate an involuntary spill of mining waste. The contaminated soils were treated with the organic amendments to study the sorption, desorption, and distribution of Cu in a period of 30 days. The application of simple procedures such as alkalinization or washing of the agro-industrial wastes improved the Cu sorption capacity and facilitated the application of these materials to the soil. The application of mine tailings to the soils decreased the Cu sorption and the affinity of the substrate for the metal. This adverse effect was ameliorated by the incorporation of minimally treated olive mill wastes and grape stalks, increasing the sorption by a range of 15 to 75% compared to untreated soils. In substrates with sandy loam soil, both amendments decrease the soluble fraction of Cu, an effect that was not observed in clay soil. In parallel, both amendments increased the fraction of metal bound to the oxidizable fraction, an effect that was greater for grape stalks. The organic amendments used in this study were effective to reduce the initial contamination by copper after a spill of mine tailing wastes containing this metal. In this sense, both amendments applied to sandy loam soil increased the organic matter content and the Cu sorption capacity, effects that are maintained for at least 30 days. In clay soil, these effects were observed only for grape stalks, probably due to its greater metal sorbent capacity compared to the olive oil waste.