We propose a dense tensor accelerator called VectorMesh, a scalable, memory-efficient architecture that can support a wide variety of DNN and computer vision workloads. Its building block is a tile execution unit~(TEU), which includes dozens of processing elements~(PEs) and SRAM buffers connected through a butterfly network. A mesh of FIFOs between the TEUs facilitates data exchange between tiles and promote local data to global visibility. Our design performs better according to the roofline model for CNN, GEMM, and spatial matching algorithms compared to state-of-the-art architectures. It can reduce global buffer and DRAM fetches by 2-22 times and up to 5 times, respectively.