To address the deep coupling of power-cooling-computing multi-energy flows in data centers and the requirement for computing service compliance assurance, as well as the poor convergence and strong decision subjectivity of traditional scheduling methods when handling heterogeneous metric trade-offs, this paper proposes a cooperative scheduling method considering power usage effectiveness (PUE) convexification and engineering priority. First, a computing time window and a delay penalty mechanism are constructed to quantify task flexibility. Meanwhile, a chance-constrained model based on adaptive safety margins is established. Subsequently, an efficient PUE convexification and hierarchical sequence solving framework is designed. This framework utilizes a hierarchical sequence method to establish a “compliance-service-economy” decision-making priority, thereby avoiding the drawbacks of traditional weighting methods. Furthermore, an improved sequential convex programming (SCP) algorithm is introduced to achieve rapid optimization of the non-convex PUE model. Case studies demonstrate that the proposed method reduces the comprehensive system PUE to 1.1417 and achieves Pareto optimality between security and economy at a 95% confidence level. Compared with traditional weighting methods, the proposed strategy accurately exploits the tolerance of quality of service (QoS) while overcoming the limitation of non-convex models being prone to local optima, thereby improving computational speed by approximately 55% with an approximation error as low as 0.026%.