This study conducts alternative-basic-angle trapezoidal tearing and single-edge notch tearing tests on a polytetrafluoroethylene coated woven fabric, where the two methods are related through the basic angle of a trapezoid. The tearing process and failure modes are carefully examined, and load–displacement curves and tearing strength are analyzed. The tearing process comprises three stages, which are distinguished photographically or in different load–displacement curve sections. Corresponding to these stages, failure modes can be classified into three parts with varying extension directions. The effect of the basic angle is clearly illustrated. As the angle increases, three stages and parts appear in sequence; the tearing strength increases, but the larger one changes from weft to warp. The relationship between the tearing process and tearing strength is described. The three stages correspond to the increase in tearing strength, occurrence of the maximum tearing strength, and failure. Because the single-edge notch tearing method is more complex and important, it is the method that is studied mainly. Digital image correlation equipment is used to observe the strain distribution at the crack section. Moreover, the applications of four frequently used models are investigated. The results indicate that Thiele’s empirical formula offers the best simulation among the three tearing strength prediction models, and the theoretical stress distribution model also provides good simulation. Furthermore, a numerical simulation is conducted. The critical tearing strength and load–displacement curves before tearing initiates acquired through the simulation and test agree well. All results may provide basic data for future improvements in design theories.