Spatial heterodyne Raman spectroscopy is a spectroscopic detection technique that is particularly suitable for Raman measurements. The spectral range of traditional spatial heterodyne Raman spectrometer (SHRS) is limited by its spectral resolution and the number of detector elements. We propose an SHRS with an echelle-mirror structure that employs multiple diffraction orders to achieve a broad spectral coverage and high spectral resolution simultaneously. This SHRS is used to obtain the Raman spectra of organic liquids, inorganic solid targets, and mixed targets. Observations of aqueous solutions, and minerals are presented. In addition, anti-Stokes Raman shifts are also presented. The proposed SHRS technique shows good performance for broadband, high-resolution Raman measurements.