A simple one-step method is presented for fabricating inorganic nanosponges with a kaolinite [Al2Si2O5(OH)4] structure. The nanosponges were synthesized by the hydrothermal treatment of aluminosilicate gels in an acidic medium (pH = 2.6) at 220 °C without using organic cross-linking agents, such as cyclodextrin or polymers. The formation of the nanosponge morphology was confirmed by scanning electron microscopy, and the assignment of the synthesized aluminosilicates to the kaolinite group was confirmed by X-ray diffraction and infrared spectroscopy. The effect of the synthesis conditions, in particular, the nature (HCl, HF, NaOH, and H2O) and pH of the reaction medium (2.6, 7, and 12), as well as the duration of the synthesis (3, 6, and 12 days), on the morphology of aluminosilicates of the kaolinite group was studied. The sorption capacity of aluminosilicate nanosponges with respect to cationic (e.g., methylene blue) and anionic (e.g., azorubine) dyes in aqueous solutions was studied. The pH sensitivity of the surface ζ potential of the synthesized nanosponges was demonstrated. The dependence of the hemolytic activity (the ability to destroy erythrocytes) of aluminosilicate nanoparticles on the particle morphology (platy, spherical, and nanosponge) has been identified for the first time. Aluminosilicate nanosponges were not found to exhibit hemolytic activity. The prospects of using aluminosilicate nanosponges to prepare innovative functional materials for ecology and medicine applications, in particular, as matrices for drug delivery systems, were identified.