Ultra-reliable low-latency communication (URLLC) and enhanced mobile broadband (eMBB) are two types of services with delay quality of service (QoS) demands. Considering the random and sporadic URLLC packets arrival feature, slicing puncture is believed to be the suitable method to support co-existence communication scenario of eMBB and URLLC terminals. However, slicing puncture in a short time is not trivial, and needs accurate wireless resource scheduling. At the same time, it may damage the QoS of eMBB service. All of these make the QoS guaranteed scheduling problem more challenging. In this paper, we investigate the bandwidth, power allocations, slice puncturing problems to find the way satisfying services’ individual QoS demands. For scheduling of eMBB service, we formulate a joint optimization problem for bandwidth and power allocations with long-term constraints of queues backlog. To solve this problem, we utilize the Lyapunov drift-plus-penalty method to establish the relationship between the long-term constraints and the short-term optimization problem, which means that the long-term constraints are gradually satisfied by the proposed strategy at each step. We further divide the short-term optimization problem into two subproblems, and adopt Block Coordinate Descent (BCD) algorithm to reduce the computation complexity. Then, we put forward a one-to-one matching method to solve the integer programming in resource block allocation and slicing puncture problems. Numerical results demonstrate that the proposed dynamic resource allocation and puncturing strategy (DRAPS) can solve the scheduling problem of eMBB and URLLC services in the presence of multiple randomnesses of channel state information (CSI) and URLLC packets arrival.