Exemption
Exempt
noun, verbal noun
To excuse and to exclude, that's exemption.
免除 means granting relief or exemption from a duty or obligation that would otherwise be required, like paying tuition fees, repaying debts, obtaining specific licenses for certain activities, and so on.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
私の祖父は心臓病を患っていたため、兵役を免除されました。
My grandfather was exempt from military service because he had a heart disease.