This paper presents an optically wavelength-tunable and intensity-switchable dye-doped cholesteric liquid crystal (DDCLC) spherical microlaser with an azo-chiral dopant. Experimental results present that two functions of optical control - tunability of lasing wavelength and switchability of lasing intensity - can be obtained for this spherical microlaser at low and high intensity regimes of non-polarized UV irradiation, respectively. If the DDCLC microdroplet is subjected to weak UV irradiation, azo-chiral molecules may transform to the bent cis state at a low concentration rate. The effect can slightly decrease the local order of LCs and thus the helical twisting power of the CLC in the microdroplet. As a result, the CLC pitch may become slightly elongated, which will cause the gradual red-shift of both omnidirectional PBG and lasing emission of the DDCLC spherical microdroplet. In contrast, when the microdroplet is subjected to strong UV irradiation, numerous azo-chiral molecules may simultaneously change to bent cis-isomers to seriously disarrange the helical texture of the CLC, which will quickly deform the PBG and deactivate the lasing emission of the microdroplet. Prolonged irradiation of a blue beam after strong UV irradiation may cause the cis azo-chiral molecules quickly convert back rod-like trans-isomers, which may then regenerate the CLC Bragg onion and PBG structures and reactivate the lasing emission of the microdroplet. Optical control of the DDCLC spherical microlaser is realized on a scale of seconds and minutes when UV irradiation is strong and weak, respectively. The 3D DDCLC spherical microlaser is a highly promising controllable 3D micro-light source or microlaser (e.g., all-optical 3D single photon microlaser) for applications of 3D all-optical integrated photonics, laser displays, and biomedical imaging and therapy, and as a 3D UV microdosagemeter or microsensor.