Hollow beam is an important structured light and also one of the hot research topics in the field of light field manipulation. As a typical hollow beam, Laguerre-Gaussian beam is also named vortex beam because of its helical phase. Moreover, because of carrying orbital angular momentum, vortex beam is tremendously valuable in optical communication, quantum entanglement and super-resolution imaging. In this work, based on the all-solid-state two-mirror concave-plane Nd:YVO4 laser experimental platform,the continuous-wave 16th-order vortex laser is obtained by fabricating some spot defects onto the output coupler to suppress the low-order Gaussian mode and force the operation of high-order Laguerre-Gaussian vortex laser. A maximum output power of 280 mW is achieved with a slope efficiency of 18.6% at an absorbed power of 3.3 W. Furthermore, a passive Q-switched high-order Laguerre-Gaussian laser with positive and negative handedness is demonstrated for the first time by inserting a Cr:YAG crystal into the laser cavity as a saturable absorber, and the shortest pulse width of the pulsed laser is 232 ns at a repetition rate of 229.1 kHz. The research indicates that spot defect mirror is a stable and reliable measures for direct generation of high-order vortex lasers. Moreover, it can be combined with other solid-state laser technology such as passive Q switching to produce spatially structured light operating at different regimes.