Mesoporous tungsten-silicates, W-MMM-E, have been prepared following evaporation-induced self-assembly methodology and characterized by elemental analysis, XRD, N2 adsorption, STEM-HAADF (high angle annular dark field in scanning-TEM mode), DRS UV-vis, and Raman techniques. DRS UV-vis showed the presence of two types of tungsten oxo-species in W-MMM-E samples: isolated tetrahedrally and oligomeric octahedrally coordinated ones, with the ratio depending on the content of tungsten in the catalyst. Materials with lower W loading have a higher contribution from isolated species, regardless of the preparation method. W-MMM-E catalyzes selectively oxidize of a range of alkenes and organic sulfides, including bulky terpene or thianthrene molecules, using green aqueous H2O2. The selectivity of corresponding epoxides reached 85–99% in up to 80% alkene conversions, while sulfoxides formed with 84–90% selectivity in almost complete sulfide conversions and a 90–100% H2O2 utilization efficiency. The true heterogeneity of catalysis over W-MMM-E was proved by hot filtration tests. Leaching of inactive W species depended on the reaction conditions and initial W loading in the catalyst. After optimization of the catalyst system, it did not exceed 20 ppm and 3 ppm for epoxidation and sulfoxidation reactions, respectively. Elaborated catalysts could be easily retrieved by filtration and reused several times with maintenance of the catalytic behavior.