Stevia is the common word to refer to the plant stevia rebaudiana which is the sweetest of the stevia species of plants and historically used as a sweetening agent. This sweetness is traced back to glycoside (bound to sugar) compounds of steviol, with the two most important steviol glycosides being stevioside and rebaudioside A.
Unlike other sweetening agents such as aspartame or sucralose, ingestion of stevia in feasible doses confers pharmacological activity. Ingestion of either stevioside or rebaudioside A will result in a circulating level of steviol and its conjugate (steviol glucuronide) which can then exert effects in the body.
In low doses, stevia consumption appears to be associated with general anti-inflammatory and anti-oxidative effects; these effects have been linked to protection of the kidneys, pancreas, liver, and brain when they precede damaging stressors (so although there is some organ protective effects, it is merely due to the general properties of steviol rather than a unique mechanism). Higher doses appear to be linked to fertility problems in animals, and although it is somewhat contested of an issue (some studies in male rats not showing anti-fertility actions, lack of human studies) it may be prudent to not overconsume stevia due to this.
In regards to the genotoxic effects, although overconsumption (or selective choosing of bacterial plates to conduct an Ames test in) is associated with genotoxic effects the potency of this genotoxic effect when it occurs appears to be quite minimal. Cancer causing effects of stevia overconsumption may not be overly relevant due to the low potency of the steviol glycosides and the inherent antioxidant properties also conferring a protective effects (perhaps regulating its own genotoxicity, definitely reduces the reliability) and as such should not be too much of a concern.