The dominant treatment process for removing heavy metals from industrial wastewater is chemical neutralisation precipitation using lime milk as a precipitation agent, resulting in a highly voluminous hydroxide sludge with a low heavy metal concentration. These sludges are predominantly landfilled, and the metals are lost to the circular economy. At the same time, metals are urgently needed as raw materials. A new approach is represented by the low-pressure, low-energy Specific Product-Oriented Precipitation process (SPOP). This approach, however, requires the adjustment of various reaction parameters for optimal operation. This study presents the impacts of the stirring rate during the reaction and the Fe concentration in the solution on the recovery of Cu from Cu-enriched electroplating wastewater. Three different recovery options are described: Option (1), the formation of CuO; Option (2), the generation of brochantite, a Cu-hydroxysulphate; and Option (3), the incorporation of Cu into ferrite. Tenorite (CuO) is precipitated at 40 °C reaction temperature at a low stirring rate of 100–200 rpm. At an accelerated stirring rate of 400–500 rpm, brochantite (Cu4(OH)6SO4) is formed. With high Fe concentrations and a molar ratio of Cu:Fe of 1:2, Cu-ferrite (CuFe2O4) is the precipitation product. In any case, the achieved recovery rates in the treated wastewater are better than 99.9%.