In order to study the meso-mechanical properties and instability mechanism of concrete-granite composite under uniaxial compression, based on the particle flow, the uniaxial compression numerical tests under the coupling of different joint shapes and joint dip angles were carried out. The evolution characteristics of strength, deformation parameters and micro-crack propagation law of the composite were compared and analyzed. The energy evolution damage characteristics were revealed, and the instability index of the composite considering the energy form was proposed. The results show that the elastic modulus of the composite specimen gradually decreases first and then increases sharply, showing a “U” shape change characteristic, and the peak stress shows a “V” shape change characteristic that decreases first and then increases. With the increase of joint dip angle, the failure modes of the composite are divided into three types: tensile shear failure, oblique tensile failure and splitting shear failure. When the joint dip angle of the composite is 90°, the damage parameter D changes fastest, the damage characteristics of the composite are the most obvious, and the stability is the worst. Under different joint shapes, when the joint dip angles are 0°, 30°and 45°, the damage characteristics of the triangular joint shape sample are the most obvious. The average instability values of concrete-granite composite specimen under different working conditions have the same variation law, which gradually decreases with the increase of joint dip angle. Only when the trapezoidal joint dip angle is 60°−90°, the average instability value of the composite specimen increases slightly. The larger the joint dip angle is, the more likely the composite specimen is to instability. With the increase of the joint dip angle, the average instability value S of the trapezoidal joint composite specimen increases significantly, which can be used as a sensitive index to determine its stability. The research results can provide reference for the safe construction of tunnel (roadway) engineering.