Mobile edge computing (MEC) is expected to be an effective solution to deliver 360-degree virtual reality (VR) videos over wireless networks. In contrast to previous computation-constrained MEC framework, which reduces the computation-resource consumption at the mobile VR device by increasing the communication-resource consumption, we develop a communications-constrained MEC framework to reduce communication-resource consumption by increasing the computation-resource consumption and exploiting the caching resources at the mobile VR device in this paper. Specifically, according to the task modularization, the MEC server can only deliver the components which have not been stored in the VR device, and then the VR device uses the received components and the corresponding cached components to construct the task, resulting in low communication-resource consumption but high delay. The MEC server can also compute the task by itself to reduce the delay, however, it consumes more communication-resource due to the delivery of entire task. Therefore, we then propose a task scheduling strategy to decide which computation model should the MEC server operates, in order to minimize the communication-resource consumption under the delay constraint. Finally, we discuss the tradeoffs between communications, computing, and caching in the proposed system.