In this paper, a dynamic spectrum management framework is proposed to improve spectrum resource utilization in a multi-access edge computing (MEC) in autonomous vehicular network (AVNET). To support the increasing data traffic and guarantee quality-of-service (QoS), spectrum slicing, spectrum allocating, and transmit power controlling are jointly considered. Accordingly, three non-convex network utility maximization problems are formulated to slice spectrum among BSs, allocate spectrum among autonomous vehicles (AVs) associated with a BS, and control transmit powers of BSs, respectively. Via linear programming relaxation and first-order Taylor series approximation, these problems are transformed into tractable forms and then are jointly solved through an alternate concave search (ACS) algorithm. As a result, optimal spectrum slicing ratios among BSs, optimal BS-vehicle association patterns, optimal fractions of spectrum resources allocated to AVs, and optimal transmit powers of BSs are obtained. Based on our simulation, a high aggregate network utility is achieved by the proposed spectrum management scheme compared with two existing schemes.