Acceleration and manipulation of electron bunches underlie most electron and X-ray devices used for ultrafast imaging and spectroscopy. New terahertz-driven concepts offer orders-of-magnitude improvements in field strengths, field gradients, laser synchronization and compactness relative to conventional radio-frequency devices, enabling shorter electron bunches and higher resolution with less infrastructure while maintaining high charge capacities (pC), repetition rates (kHz) and stability. We present a segmented terahertz electron accelerator and manipulator (STEAM) capable of performing multiple high-field operations on the 6D-phase-space of ultrashort electron bunches. With this single device, powered by few-micro-Joule, single-cycle, 0.3 THz pulses, we demonstrate record THz-acceleration of >30 keV, streaking with <10 fs resolution, focusing with >2 kT/m strength, compression to ~100 fs as well as real-time switching between these modes of operation. The STEAM device demonstrates the feasibility of THz-based electron accelerators, manipulators and diagnostic tools enabling science beyond current resolution frontiers with transformative impact.