Primitive photosynthetic microorganisms, either dormant or dead, may remain today on the martian surface, akin to terrestrial cyanobacteria surviving endolithically in martian analog sites on Earth such as the Antarctic Dry Valleys and the Atacama Desert. Potential markers of martian photoautotrophs include the red edge of chlorophyll reflectance spectra or fluorescence emission from systems of light-harvesting pigments. Such biosignatures, however, would be modified and degraded by long-term exposure to ionizing radiation from the unshielded cosmic ray flux onto the martian surface. In this initial study into this issue, three analytical techniques--absorbance, reflectance, and fluorescence spectroscopy--were employed to determine the progression of the radiolytic destruction of cyanobacteria. The pattern of signal loss for chlorophyll reflection and fluorescence from several biomolecules is characterized and quantified after increasing exposures to ionizing gamma radiation. This allows estimation of the degradation rates of cyanobacterial biosignatures on the martian surface and the identification of promising detectable fluorescent break-down products.