What is the net electrical charge on a magnesium ion that is formed when a neutral atom loses two electrons?

Per electron lost an atom gains a + 1 charge. Since 2 electrons are lost the magnesium ion has a 2 + charge.

This magnesium ion will have a charge of + 2. This is because it retained the same number of protons and neutrons, but the loss of 2 electrons (with negative charge) means that there are now 2 extra protons compared to electrons, and those 2 protons give a net charge of + 2.