Particle accelerators that use electromagnetic fields to increase a charged particle's energy have greatly advanced the development of science and industry since invention. However, the enormous cost and size of conventional radio-frequency accelerators have limited their accessibility. Here, we demonstrate a miniaccelerator powered by terahertz pulses with wavelengths 100 times shorter than radio-frequency pulses. By injecting a short relativistic electron bunch to a 30-mm-long dielectric-lined waveguide and tuning the frequency of a 20-period terahertz pulse to the phase-velocity-matched value, precise and sustained acceleration for nearly 100% of the electrons is achieved with the beam energy spread essentially unchanged. Furthermore, by accurately controlling the phase of two terahertz pulses, the beam is stably accelerated successively in two dielectric waveguides with close to 100% charge coupling efficiency. Our results demonstrate stable and scalable beam acceleration in a multistage miniaccelerator and pave the way for functioning terahertz-driven high-energy accelerators.