Computing with high-dimensional (HD) vectors, also referred to as $\textit{hypervectors}$, is a brain-inspired alternative to computing with scalars. Key properties of HD computing include a well-defined set of arithmetic operations on hypervectors, generality, scalability, robustness, fast learning, and ubiquitous parallel operations. HD computing is about manipulating and comparing large patterns-binary hypervectors with 10,000 dimensions-making its efficient realization on minimalistic ultra-low-power platforms challenging. This paper describes HD computing's acceleration and its optimization of memory accesses and operations on a silicon prototype of the PULPv3 4-core platform (1.5mm$^2$, 2mW), surpassing the state-of-the-art classification accuracy (on average 92.4%) with simultaneous 3.7$\times$ end-to-end speed-up and 2$\times$ energy saving compared to its single-core execution. We further explore the scalability of our accelerator by increasing the number of inputs and classification window on a new generation of the PULP architecture featuring bit-manipulation instruction extensions and larger number of 8 cores. These together enable a near ideal speed-up of 18.4$\times$ compared to the single-core PULPv3.