Innovative terahertz waveguides are in high demand to serve as a versatile platform for transporting and manipulating terahertz signals for the full deployment of future six-generation (6G) communication systems. Metal-wire waveguides have emerged as promising candidates, offering the crucial advantage of sustaining low-loss and low-dispersion propagation of broadband terahertz pulses. Recent advances have opened up new avenues for implementing signal-processing functionalities within metal-wire waveguides by directly engraving grooves along the wire surfaces. However, the challenge remains to design novel groove structures to unlock unprecedented signal-processing functionalities. In this study, we report a plasmonic signal processor by engineering topological interface states within a terahertz two-wire waveguide. We construct the interface by connecting two multiscale groove structures with distinct topological invariants, i.e., featuring a π-shift difference in the Zak phases. The existence of this topological interface within the waveguide is experimentally validated by investigating the transmission spectrum, revealing a prominent transmission peak in the center of the topological bandgap. Remarkably, we show that this resonance is highly robust against structural disorders, and its quality factor can be flexibly controlled. This unique feature not only facilitates essential functions such as band filtering and isolating but also promises to serve as a linear differential equation solver. Our approach paves the way for the development of new-generation all-optical analog signal processors tailored for future terahertz networks, featuring remarkable structural simplicity, ultrafast processing speeds, as well as highly reliable performance.