Extending the high-harmonic cutoff with experimentally accessible fields is essential for advancing tabletop coherent extreme-ultraviolet (EUV) and soft-x-ray sources. Although terahertz (THz) assistance offers a promising route, cutoff extension at weak-to-moderate, laboratory-accessible THz strengths remains poorly understood. In this Letter, we investigate THz-assisted high-order harmonic generation (HHG) using time-dependent Schrödinger equation simulations supported by classical trajectory, quantum-orbit theory, and Bohmian dynamics. We demonstrate that even weak-to-moderate THz fields extend the cutoff, producing a pronounced “fish-fin” structure whose dominant branches saturate near $I_p+8U_p$. We attribute this extension to long electron excursions spanning multiple optical cycles before recombination. This cutoff-extension mechanism is robust across atomic species and driving parameters, indicating that laboratory-scale THz fields enable practical cutoff control and access to high-energy HHG.

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• High-order harmonic generation
• Light-matter interaction
• Nonlinear optics