Despite numerous studies on the influence of heavy metals on soil health, the search for effective, eco-friendly, and economically viable remediation substances is far from over. This encouraged us to carry out a study under strictly controlled conditions to test the effects of Cu2+, Ni2+, and Zn2+ added to soil in amounts of 150 mg·kg−1 d.m. of soil on the soil microbiome, on the activity of two oxidoreductases and five hydrolases, and on the growth and development of the sunflower Helianthus annunus L. The remediation substances were a molecular sieve, halloysite, sepiolite, expanded clay, zeolite, and biochar. It has been demonstrated that the most severe turbulences in the soil microbiome, its activity, and the growth of Helianthus annunus L. were caused by Ni2+, followed by Cu2+, and the mildest negative effect was produced by Zn2+. The adverse impact of heavy metals on the soil microbiome and its activity was alleviated by the applied sorbents. Their application also contributed to the increased biomass of plants, which is significant for the successful phytoextraction of these metals from soil. Irrespective of which property was analysed, sepiolite can be recommended for the remediation of soil polluted with Ni2+ and zeolite—for soil polluted with Cu2+ and Zn2+. Both sorbents mitigated to the highest degree disturbances caused by the tested metals in the soil environment.