In this study, activated carbons derived from walnut shells (CA-N) and apple wood (CA-M) were used as adsorbents to remove cobalt(II) and strontium(II) ions from aqueous solutions. The novel materials were obtained using nitric acid (CA-Mox) and nitric acid/urea mixture (CA-Mox-u, CA-Nox-u) as oxidizing agents. The physical–chemical characteristics of activated carbons were determined from nitrogen sorption isotherms, SEM-EDX, FTIR, pH metric titrations, the Boehm titration method and elemental analysis. The results of batch experiments indicate that maximum adsorption can be achieved in broad pH ranges: 4–8 for Co(II) and 4–10 for Sr(II). The maximum adsorption capacities of Co(II) and Sr(II) on oxidized activated carbons at pH = 4 are: CA-Mox, 0.085 and 0.076 mmol/g; CA-Mox-u, 0.056 and 0.041 mmol/g; and CA-Nox-u, 0.041 and 0.034 mmol/g, respectively. The mathematical models (pseudo-first-order, pseudo-second-order and intraparticle diffusion kinetic models, and Langmuir, Freundlich, Dubinin–Radushkevich, and Temkin–Pyzhev isotherm models) were used to explain the adsorption kinetics, to study the adsorption mechanism and predict maximum adsorption capacity of the adsorbents. The adsorption mechanisms of toxic metal ions on activated carbons were proposed.