Mechanically tunable Bragg filters at terahertz frequencies are designed, fabricated by a simple procedure, and characterized via THz time-domain spectroscopy. The Bragg reflectors are composed by stacking thin cyclo-olefin Zeonor polymer layers, which are separated by spacers made of a bi-adhesive tape. The defect cavity is void and its thickness is mechanically tuned by means of a translation stage. The filters show high transmittance and quality factors, owing to the selected very low-loss polymer.