SiC-fiber-reinforced Al-Mg matrix composites with different mass fractions of Mg were fabricated by combining colloidal dispersion with a squeeze melt infiltration process. The microstructure, mechanical and damping properties, and the corresponding mechanisms were investigated. Microstructure analyses found that SiCf/Al-Mg composites presented a homogeneous distribution of SiC fibers, and the relative density was higher than 97% when the mass fraction of Mg was less than 20%; the fiber–matrix interface bonded well, and no obvious reaction occurred at the interface. The SiCf/Al-10Mg composite exhibited the best flexural strength (372 MPa) and elastic modulus (161.7 GPa). The fracture strain of the composites decreased with an increase in the mass fraction of Mg. This could be attributed to the strengthened interfacial bonding due to the introduction of Mg. The damping capacity at RT increased dramatically with an increase in the strain when the strain amplitude was higher than 0.001%, which was better than the alloys with similar composition, demonstrating a positive effect of the SiC fiber on improving the damping capacity of composite; the damping capacity at a temperature beyond 200 °C indicated a monotonic increase tendency with the testing temperature. This could be attributed to the second phase, which formed more strong pinning points and increased the dislocation energy needed to break away from the strong pinning points.