Direct initiation of secondary explosives by a semiconductor laser is highly demanded, but it is challenging to exclude the use of sensitive primers. Most laser-sensitive energetic materials are usually mechanically sensitive. In order to reduce the mechanical sensitivity (MS) of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) while improving laser absorbance in the near-infrared band, spherical CL-20 composites (SCCs) embedded with nano aluminum (Al) powder and graphene-based catalyst (GO-CHZ-Co) were prepared by a spray drying method. These SCCs have been characterized comprehensively in terms of their morphologies, particle size distribution, laser absorbance, thermal decomposition behaviors, MS, and laser ignition properties. Results show that the maximum critical impact energy of SCCs was 3.8 J, which is 2.8 J higher than that of pristine ε-CL-20. The critical friction load was increased by at most 108 N compared to pristine CL-20. The absorbance has also been significantly increased up to almost 70% in the wavelength between 400 and 1400 nm, where the peak absorption is located in the region of 800–900 nm. In addition, the initial decomposition temperature (Ti) of SCCs is lower than that of pure CL-20, especially in the presence of GO-CHZ-Co. The apparent activation energy (Ea) for the decomposition of SCCs was largely dependent on the particle size of Al. Preliminary ignition tests indicate that the SCCs can be ignited successfully by a small-power laser.