Plasmon-based devices are powerful for use in highly sensitive evanescent-field detection and analysis, but they exhibit the problem of limited frequency tunability for fixed structures. This feature causes problems in the multi-frequency investigations required for materials characterization, bio-related research, etc. Here, we propose and fabricate a spiral-shaped plasmonic structure that enables a continuous frequency-tuneable evanescent-field concentration in the terahertz (THz) region with simple operation. The device also increases the electric field intensity at the subwavelength aperture, thus significantly amplifying the transmission. Highly tuneable transmission bands are observed by simply rotating the spiral plasmonic structure, which are in good agreement with the behaviour expected from electromagnetic simulation. Medical examinations are performed by measuring the interactions between the frequency-tuneable plasmons and bio-samples, which enables observing distinct tissue-dependent transmission spectra and images. The developed device simultaneously offers the advantages of both plasmonic devices and frequency-tuneable devices, which can increase the availability and versatility of evanescent-field THz sensing and analysis. The mechanism presented will shed light on THz plasmonics and motivate the implementation of a variety of applications based on plasmon-mediated THz technologies.