A composite of a knitted fabric and a soft matrix enables applications that require low stiffness and high crack resistance. Examples include heart valves and stretchable strain sensors. Here we study processes of crack growth in such a composite under monotonic and cyclic stretch. We fabricate a composite using a knitted fabric of nylon yarn and an elastomer matrix of polycarbonate urethane. We precut a sample with a crack, monotonically stretch the sample, and observe the growth of the crack. The crack grows in the matrix as the yarn slips and breaks. The stretch is converted to energy release rate G. We identify two critical energy release rates, GA and GB. When G < GA, the yarn does not slip, and the crack does not grow in the matrix. When GA < G < GB, the yarn slips but does not break, and the crack grows in the matrix stably and arrests when the stretch stops increasing. When G = GB, the yarn slips and breaks, while the crack grows unstably. When the sample is subject to cyclic stretch, we observe analogous behavior of crack growth and arrest, as well as yarn slip and yarn break. However, the two critical values, Ga and Gb, are much smaller than the corresponding values under monotonic stretch.