Manufactured sand (MS) is a promising alternative aggregate to quartz sand (QS) in ultra-high-performance concrete (UHPC) in the preparation of ultra-high-performance manufactured sand concrete (UHPMC), which possesses the characteristics of high strength, low cost, and environmental friendliness. In this study, the effects of variable compositional characteristics including the water–binder ratio, the stone powder (SP) content, and the MS replacement ratio on the mechanical and flexural strength of UHPMC were compared and analyzed based on response surface methodology (RSM). Meanwhile, the damage characteristics of UHPMC during compressive and flexural stress were monitored and evaluated using acoustic emission (AE) technology. The results reveal that the compressive and flexural strengths of UHPMC are both negatively correlated with the water–binder ratio, while they are positively correlated with the MS replacement rate. They tend to firstly increase and subsequently decrease with the increase in the stone powder content. In the load–displacement curve of concrete with a high MS replacement ratio and a low water–binder ratio, the slope in the elastic stage is steeper, the stiffness is higher, and the bending toughness and ductility are also better. The specimens with a 10% to 0% stone powder content present a steeper elastic phase slope, a slightly higher stiffness, and superior ductility. The specimens with a low MS replacement ratio and a high water–binder ratio display earlier cracking and weaker resistance, and the destruction process is complex and very unstable. The damage mode analysis based on RA-AF shows that an increase in the MS replacement ratio and a decrease in the water–binder ratio can both reduce the tensile cracking of UHPMC specimens under a four-point bending test. Although 10% stone powder can marginally slow down crack growth, the failure mode is not significantly affected.