Question: Mana is the substance that makes a human capable of performing spells. In the magitocracy, mages rule the kingdom. An individual capable of magic must learn to focus his power, solidifying and controlling the Mana in order to use it. Welding Mana in this way takes years of study. Mages are of various power levels, those who master their Mana welding are among the strongest mages in society.

However, there are areas of the world in which Mana roams free and unbound by humans. This mana is unrestrained and leads to these areas being high in radiation. This could be deadly to those in the vicinity, as it can have debilitating effects, mutations, and even death.

All humans contain Mana, whether they learn to harness it or not. However, Wild Mana remains dangerous to people. How could this be the case?

Answer: 
It causes elements to transmute into other forms.

Turning lead into gold is a classic pursuit of magic, and so is turning carbon to silicon (through petrification), but both of these do not change the number of nucleons in the atom -- they change whether they are protons or neutrons.

Very little change is needed to make radically unstable atoms. And the wild magic, not being constrained by a mage, tends to be rather more random in its changes. (Iron into sodium? Why not? Which means that it's not only radioactive but before it decays, it's explosive in the presence of water.)

(Poul Anderson made use of the "silicon" idea.)
Mana is energy. Even though some animals have organs that process mana, much like the electric eel does for electricity, in excessive amounts, it is *always* dangerous. Well-trained mages can supplement their own biological reserves by drawing from a low level of ambient mana, but excessive use can cause shock, organ failure, even death.

Drawing mana inside yourself can have all sorts of unpredictable magical effects if you aren't able to control it, including visible physical changes but also subtler effects on bio-thaumatology, which is why even non-mages who wish to work in high-mana areas must have some degree of magic training. The changes might be reversible by a specialist, but that does you no good if you die before you get to one or didn't know you were affected. Extreme levels of environmental mana is dangerous even to well-trained mages in the best PPE.