We present the VIMOS Spectroscopic Survey of a Supercluster in the COSMOS field (VIS3COS) at z ∼ 0.84. We use VIMOS high-resolution spectra (GG475 filter) to spectroscopically select 490 galaxies in and around the superstructure and an additional 481 galaxies in the line of sight. We present the redshift distribution, the catalogue to be made public, and the first results on the properties of individual galaxies and stacked spectra (3500 Å < λ <  4200 Å rest-frame). We probe a wide range of densities and environments (from low-density field to clusters and rich groups). We find a decrease in the median star formation rate from low- to high-density environments in all bins of stellar mass and a sharp rise of the quenched fraction (from ∼10% to ∼40 − 60%) of intermediate-stellar-mass galaxies (10 <  log10 (M⋆/M⊙) <  10.75) from filaments to clusters. The quenched fraction for massive galaxies shows little dependence on environment, being constant at ∼30 − 40%. We find a break in the strength of the [O II] emission, with nearly constant line equivalent widths at lower densities (∼ − 11 Å) and then a drop to ∼ − 2.5 Å towards higher densities. The break in the [OII] line strength happens at similar densities (log10(1 + δ) ∼ 0.0 − 0.5) as the observed rise in the quenched fraction. Our results may provide further clues regarding the different environmental processes affecting galaxies with different stellar masses and highlight the advantages of a single dataset in the COSMOS field probing a wide range of stellar masses and environments. We hypothesise that quenching mechanisms are enhanced in high-density regions.