We report a terahertz quantum-cascade vertical-external-cavity surface-emitting laser (QC-VECSEL) whose output power is scaled up to watt-level by using an amplifying metasurface designed for increased power density. The metasurface is composed of a subwavelength array of metal-metal waveguide antenna-coupled sub-cavities loaded with a terahertz quantum-cascade gain material. Unlike previously demonstrated THz QC-VECSELs, the sub-cavities operate on their third-order lateral modal resonance (TM03), instead of their first-order (TM01) resonance. This results in a metasurface with a higher spatial density of the gain material, leading to an increased output power per metasurface area. In pulsed mode operation, peak THz output powers up to 830 mW at 77 K and 1.35 W at 6 K are observed, while a single-mode spectrum and a low divergence beam pattern are maintained. In addition, piezoelectric control of the cavity length allows approximately 50 GHz of continuous, single-mode tuning without a significant effect on output power or beam quality.