Carbonate manufactured sand (crushed sand from natural rock) offers an alternative to river and quartz sands in ultra-high-performance concrete (UHPC). This study compared calcite–dolomite sand with calcite-dominated sand. X-ray diffraction and fluorescence characterized mineralogical and chemical compositions. Total organic carbon analysis assessed apparent adsorption of a polycarboxylate ether superplasticizer (PCE). Flowability, fresh rheological properties, strengths, and cross-sectional visible porosity were evaluated at water-to-binder (w/b) ratios of 0.17, 0.16, and 0.15. The calcite–dolomite sand showed a 2.23% higher gradation-weighted apparent PCE adsorption index than the calcite-dominated sand. At w/b = 0.15, UHPC containing calcite–dolomite sand had a 6.45% lower flow spread, a 61.7% longer T500, a 17.5% higher dynamic yield stress, a 21.5% higher plastic viscosity, and a 7.0% higher visible pore area fraction than UHPC containing calcite-dominated sand. At matched w/b ratios, UHPC containing calcite–dolomite sand had 2.3–2.9% lower compressive strength than UHPC containing calcite-dominated sand; the flexural strength deficit increased from 8.0% to 16.0% as w/b decreased. Greater apparent PCE adsorption by sand may reduce dispersant availability, weaken particle dispersion, and impede air release through increased viscous resistance at low w/b ratios. A source-dependent effective PCE dosage window is proposed as a conceptual framework.