I am not an expert on this subject but I can give you my opinion. Mouth cancer like all other cancers are caused my mutation in DNA which leads to uncontrollable growth of cells. These cells can invade and damage surrounding tissues. in the case of mouth cancer the areas affected are lips, gum, tongue and the mouth. The exact cause of cancer is still being researched but we have an idea of some risk factors like smoking and excessive alcohol intake, but i have not heard deep kissing as a risk factor.
Having said that, there are other infections that can be spread by deep kissing, simply because it involves exchange of body fluids. Examples of infections that can be spread by kissing include herpes and viruses that cause colds. Kissing is a natural way of showing affection but be careful who you kiss.