Summing up: No, there is no evidence that snus causes mouth cancer.
No other country in the world has such a high proportion of snus users in the population as Sweden. Despite this, there is no increased incidence of oral cancer or cancer-related mortality linked to the use of snus in Sweden. This is stated in a large study on snus and oral cancer from the Karolinska Institute, which is linked below. In this study, it is even found that using 4 doses or less of snus a week actually reduces the risk of mouth cancer, Smoking, on the other hand, dramatically increases the risk of various types of cancer including mouth cancer, see link to study below.
It is easy to believe that because both cigarettes and snus contain nicotine and because snus is also placed in the mouth for a much longer time than cigarettes, snus would increase the risk of oral cancer compared to cigarettes. One reason why this is not the case is that nicotine, although addictive, is not carcinogenic and therefore using nicotine gum, for example, does not increase the risk of cancer. Tobacco can contain carcinogenic heavy metals and nitrosamines, but it is mainly when tobacco is ignited and inhaled as smoke, as is the case with smoking, that it strongly contributes to an increased risk of oral cancer.
Snus does not increase the risk of oral cancer but has an impact on oral health with a significantly increased risk of, among other things snuff lesions and gingivitis. However, these conditions are not precursors to oral or other cancers but only affect the gums.
Large study from Karolinska Institutet on snus and oral cancer can be found here
*Smoking dramatically increases risk of oral cancer study
Bengt talks about snus and oral cancer.
Bengt talks about nicotine and cancer.