This brief addresses the task assignment and group consensus problem of multi-agents with cooperative and competitive interaction under DoS attacks. Different from the traditional direct use of the original topology information, the acyclic partitioning method and generational partition method are introduced to divide the topology of a multi-agent system without spanning trees and appoint the leader of the subgroup, thereby solving the problem of task assignment. Under the processing of this algorithm, two distributed tracking controllers are designed for the multi-agent system subjected to the non-delay and multi-delay DoS attacks after eliminating redundancy and re-labeling, and some sufficient conditions are obtained for the multi-agent system to achieve group-bipartite consensus under non-periodic DoS attacks. Additionally, a block sub-diagonal coefficient matrix of the error system under a signed network is raised in this paper, which can represent the relationship between multiple agents very well. Finally, the stability of the closed-loop system is analyzed and proven by Lyapunov stability theory, exponential stability theory, and graph theory, and the effectiveness of the proposed algorithm is verified by two simulation examples.