The specific heat C and thermal conductivity κ of neutron-irradiated crystalline quartz have been measured to <~0.1 K. Four types of low-energy excitations are observed, two of which may be removed selectively by heat treatment. From the C and κ of annealed samples it is shown that the localized excitations found in vitreous silica also occur in neutron-damaged quartz. These excitations cause the unusual low-temperature behavior which is characteristic of amorphous materials. The properties of these excitations appear to remain unchanged as the total density of excitations is reduced by a factor of ~ 40. At greater dilution, the localized excitations are masked by the effects of other, unidentified excitations.