A small amount of radiation (low-dose radiation) would cause a small amount of DNA damage which can result in mutations. However, DNA damage and mutations happen all the time even without radiation exposure, because of natural processes in our bodies, and this damage is much more than the damage that occurs due to low-dose radiation (Pollycove et al. 2003; Vilenchik et al. 2003).
Our bodies respond to the small amount of damage from low-dose radiation by increasing defenses like antioxidants, DNA repair enzymes, immune system responses, apoptosis, etc. (Feinendegen et al. 2013).
The boosted defenses would reduce the DNA damage and mutations during the subsequent period. The boosted defenses would also repair and reduce not only the damage caused by the low-dose radiation but also the naturally occurring DNA damage. The naturally occurring damage is much more than that caused by low-dose radiation (Pollycove et al. 2003; Vilenchik et al. 2003) and so the net result would be reduced DNA damage and mutations some time following the exposure to low-dose radiation (Osipov et al. 2013).
Feinendegen, L. E., M. Pollycove, et al. (2013). Hormesis by low dose radiation effects: Low-dose cancer risk modeling must recognize up-regulation of protection. Therapeutic Nuclear Medicine. R. P. Baum. Heidelberg, Springer: 789-805. http://link.springer.com/chapter/10.1007/174_2012_686
Osipov, A. N., G. Buleeva, et al. (2013). "In vivo gamma-irradiation low dose threshold for suppression of DNA double strand breaks below the spontaneous level in mouse blood and spleen cells." Mutat Res 756(1-2): 141-145. http://www.ncbi.nlm.nih.gov/pubmed/23664857
Pollycove, M. and L. E. Feinendegen (2003). "Radiation-induced versus endogenous DNA damage: possible effect of inducible protective responses in mitigating endogenous damage." Hum Exp Toxicol 22(6): 290-306. http://www.ncbi.nlm.nih.gov/pubmed/12856953
Vilenchik, M. M. and A. G. Knudson (2003). "Endogenous DNA double-strand breaks: production, fidelity of repair, and induction of cancer." Proc Natl Acad Sci USA 100(22): 12871-12876. http://www.ncbi.nlm.nih.gov/pubmed/14566050