A guided-mode resonance filter (GMRF) in the terahertz (THz) band gaining narrow line width is a vigorous approach for THz biosensing and imaging. Limited by accessible low-loss materials above 1 THz, fabrication techniques, and tuning methods, a dynamically tunable THz GMRF implementing broad frequency range tunability faces great challenges. Here, by nanoimprinting a THz low-loss elastomer styrene−butadiene−styrene (SBS) film, we propose a dynamically tunable waveguide grating structure with an expanded work frequency. Utilizing simple tension field control and Poisson's ratio of elastomer, remarkable blueshift and redshift tunability could both be realized. When the SBS GMRF was elongated along the grating lines, a blueshift occurred from 2.63 to 3.29 THz under 300% strain. While applying perpendicular stretching, the redshift dramatically spanned 3.72 THz under 150% strain, presenting prominent strain sensitivity. Additionally, the microscopic phase separation of SBS makes it exhibit the characteristics of shape memory; hence, the cyclically stretched SBS GMRF maintained stable mechanical and optical performance. Hence, the elastic and shape reversible SBS-based GMRF will be a brilliant strategy for a tunable THz optical device.