Terahertz (THz) spectroscopy has been proven as an effective detection means for the label-free and nondestructive sensing of biochemical molecules based on their unique roto-vibrational transitions. However, the conventional THz spectroscopic system is unsuitable for minute material sensing due to its far-field detection scheme, low sample amount, and lack of spectral characteristics, leading to low absorption cross-sections and sensitivity. In this study, a 3D plasmonic structure based on a metal-coated woven-wire mesh (MCWM) was experimentally and numerically demonstrated for sensing trace amounts of analytes combined with THz spectroscopy. Dual sharp spectral features were exhibited in the transmission spectrum, originating from the resonant excitation of THz surface electromagnetic modes via the aperture and periodicity of the MCWM unit cell. According to the finite element simulation, an enhanced and localized surface field was formed at THz resonant frequencies and was concentrated at the metal gaps near the periodic corrugations of the MCWM, resulting in enormous resonant dip shifts caused by the tiny variations in membrane thicknesses and refractive indices. Different types and quantities of analytes, including hydrophilic biopolymer (PAA) membrane, nonuniformly distributed microparticles to mimic macro-biomolecules or cells, and electrolyte salts of PBS, were successfully identified by the MCWM sensor with the best thickness and refractive index sensitivities approaching 8.26 GHz/μm and 547 GHz/RIU, respectively. The demonstrated detection limit of thickness and molecular concentration could respectively achieve nanometer and femtomolar scales in PAA macromolecular detection, surpassing the available metallic mesh devices. The MCWM-based sensing platform presents a rapid, inexpensive, and simple analysis method, potentially paving the way for a new generation of label-free microanalysis sensors.