Because they are so widespread, the use of saponites is significant in many industries. The modification of saponite-rich clay minerals is known to improve their existing characteristics and may provide new functional properties. The objective of the present paper was to characterize the effects of adding nanosized graphene-like molybdenum (Mo) and tungsten (W) sulfides on the textural and surface characteristics of composites based on native saponite and saponite pre-modified with nanoscale magnetite. The textural characteristics were investigated by the nitrogen adsorption-desorption method and scanning electron microscopy. The total acidity, Hammett Brönsted centers, and Quasi-Equilibrium Thermo Desorption (QE-TD) Lewis centers were characteristics used to probe the acid-base properties of the modified composites. In all cases, modification proved to have a significant effect on both the surface and textural properties of the clay matrix. Modification of the native saponite by graphene-like Mo and W sulfides resulted in a decrease in the specific surface area, except a slight increase in the surface area of the magnetite-containing saponite was observed. Analysis of the acid-base characteristics of native and magnetite-modified saponite (MMS) indicated the ability of modified MoS2 and WS2 additives to alter the acid-base state of the surface. The addition of graphene-like Mo and W sulfides increased the total acidity of native and MMS, with MoS2 modification being more promising because, in almost all the samples, saponite composite materials increased the number of both Brönsted and Lewis active centers compared with WS2, which was determined by the corresponding methods. The acid-base characteristics of the saponite-containing samples, which were studied in an aqueous medium by various methods, are in good correlation with each other, and are consistent with the sorption activity of cationic and anionic dyes.