The diminished Sombor index of a graph \( G \) is defined as \[ DSO(G)=\sum \frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v}, \] where \( d_u \) and \( d_v \) are the degrees of vertices \( u \) and \( v \), and the summation goes over all pairs of adjacent vertices. Although \( DSO \) was introduced as early as in 2021, its properties were not studied so far. The present paper is aimed at filling this gap. We obtain bounds on \( DSO \), characterize the extremal graphs, and establish Nordhaus--Gaddum-type relations. In addition, we report results of numerical studies of the structure-dependency of \( DSO \) and its chemical applicability.