The growing use of titanium alloys has led to the gradual replacement of traditional processing methods by laser cutting technology, making it the preferred method for processing titanium alloy plates due to its high efficiency, precision, and adaptability. In this review, the characteristics of laser cutting technology and its application in titanium alloy plate processing are summarized, outlining several aspects of the cutting process, microstructure, and mechanical properties of the material after cutting, along with simulation predictions. Previous research categorized laser-cutting input parameters into beam parameters and process parameters, with the commonly used parameters being the laser power, cutting speed, and gas pressure. Various parameter combinations can achieve different cutting qualities, and seven indices can be used to evaluate the cutting process, with the surface roughness and slit width serving as the most common indices. Different auxiliary gases have shown a significant impact on the laser cutting quality, with commonly used gases consisting of nitrogen, argon, and air. Argon-assisted cutting generally results in better surface quality. Due to the rapid temperature change, the titanium alloy microstructure will undergo a non-diffusive martensitic phase transformation during laser cutting, producing a heat-affected zone. Experimental studies and simulations of the mechanical properties have shown that the occurrence of a martensitic phase transformation increases the hardness and residual tensile stress of the material, which reduces the fatigue strength and static tensile properties. In addition, studies have found that the more streaks appear on the cut surface, the lower the fatigue strength is, with fatigue cracks arising from the stripes. Hence, the established analytical solution model and three-dimensional finite element model can effectively predict the temperature distribution and residual stress during the cutting process. This can provide a better understanding of the high residual stress characteristics of the cutting edge and the stripe formation mechanism, allowing researchers to better explore the mechanism of laser cutting.