The use of waste materials in masonry mortars is relatively rare, as traditional formulations primarily rely on cement and lime as binders, which are not sustainable in the context of 21st-century sustainable development goals. This study investigates the effects of cement substitution with ceramic waste powder, biomass ash, and fly ash on the restrained shrinkage of masonry mortars. Eight different mortar mixtures were produced, varying the volume ratios of solid components (1:0.7:4.2 and 1:1:4) and cement replacement levels, which reached up to 50%. Compressive strength testing revealed that all mortar types met the requirements for masonry mortars used in structural applications (class M5). After 3 months of exposure to ambient temperature and humidity, specimens were visually inspected for shrinkage-induced cracks. The distribution and width of cracks were recorded, and the pull-off strength was subsequently measured. The results confirmed that both the component volume ratio and the level of cement replacement significantly influenced the appearance and propagation of cracks caused by plastic shrinkage. Notably, some of the supplementary cementitious material (SCM)-blended mortars demonstrated favorable performance, with no visible cracks after 3 months of exposure to shrinkage effects. This study highlights the potential of using waste-based SCMs to improve the shrinkage behavior of masonry mortars, contributing to more sustainable construction practices.