The structural and surface properties of natural and modified Pliocene clays from lignite mining are investigated in the paper. Chemical modifications are made using hydrofluoric acid (HF), sulfuric acid (H2SO4), hydrochloric acid (HCl), nitric acid (HNO3), sodium hydroxide (NaOH), and hydrogen peroxide (H2O2), at a concentration of 1 mol/dm3. Scanning electron microscopy is used to detect the morphology of the samples. Nitrogen adsorption isotherms were recorded to determine the specific surface area (SSA), mesoporosity, microporosity, and fractal dimensions. The raw clay has an SSA of 66 m2/g. The most promising changes in the structural properties are caused by modifications with HF or H2SO4 (e.g., the SSA increased by about 60%). In addition, the raw and modified clays are used in preliminary tests with Cu(II) sorption, which were performed in batch static method at initial Cu(II) concentrations of 25, 50, 80, 100, 200, 300, and 500 mg/dm3 in 1% aqueous suspensions of the clayey material. The maximum sorption of Cu(II) on the raw material was 15 mg/g. The structural changes after the modifications roughly reflect the capabilities of the adsorbents for Cu(II) adsorption. The modifications with HF and H2SO4 bring a similar improvement in Cu(II) adsorption, which is around 20–25% greater than for the raw material. The structural properties of investigated clays and their adsorptive capabilities indicate they could be used as low-cost adsorbents (e.g., for industrial water pretreatment).