A responsible approach towards sustainable development requires the use of environmentally friendly, low-carbon, and energy-intensive materials. One positive way is to use glass waste as a replacement for fine natural aggregate. For this purpose, the effects of adding glass cullet to the mechanical properties of mortar were carried out. The glass aggregate made from recycled post-consumer waste glass (food, medicine, and cosmetics packaging, including mostly bottles), were used. This experimental work included four different contents of fine glass cullet (5, 10, 15, and 20 wt.% of fine aggregate). The compressive, flexural, and split tensile strengths were evaluated. Moreover, the modulus of elasticity and Poisson coefficient were determined. The addition of glass sand aggregate increases the mechanical properties of mortar. When comparing the strength, the obtained improvement in split tensile strength was the least affected. The obtained effect for the increased analysed properties of the glass sand aggregate content has been rarely reported. Moreover, it was determined that by increasing the recycled glass sand aggregate content, the density of mortar decreased. In addition, the relationships between the properties for mortar containing glass sand aggregate were observed.