To reveal the dynamic response characteristic and damage-fracture evolution laws of concrete under pulse water jet impact, the numerical simulations on pulse water jets impinging concrete for different operating parameters were established based on SPH-FEM coupling algorithm and verified in this paper. The concrete-breaking effects of pulse water jet and continuous water jet were compared, and the effects of key jet parameters and concrete strength on the damage-fracture characteristics of concrete were investigated. And the damage and stress evolution laws inner concrete were revealed. The results show that there is a better concrete-breaking effect for pulse water jet by repeatedly utilizing the extremely high water-hammer pressure and effectively weakening the water-cushion effect, compared with continuous water jet. The broken pit area and the total length of main cracks decrease with the increase of pulse length, and there is an optimal pulse spacing for pulse water jet to improve the concrete-breaking effect. The broken pit area and the total length of main cracks both linearly increase with the increasing jet velocity and exponentially increase with the increasing jet diameter. As the concrete strength increases, the broken pit area shows an S-shaped curve decreasing trend and the total length of main cracks exponentially decreases. The broken pit width first rapidly increases and tends to stabilize with the increase of jet velocity and concrete strength, and changes linearly with jet diameter and is less affected by pulse length and spacing. The farther away from the jet impact center, the longer the damage cumulative period of concrete due to the jet impact energy attenuation. In horizontal direction, concrete breakage range is approximately 4–5 times of jet diameter; in vertical direction, the previous pulses will cause concrete to be destroyed or damaged, and the subsequent pulses will make the damaged concrete suffer greater stress, causing more serve damage. And the induced stress peak decreases in form of Power function with the increasing distance. The research results could provide theoretical guidance for the parameters selection of pulse water jet efficiently breaking concrete.