From Latin 'deportare' (to carry away) — exile and 'deportment' (how you carry yourself) share the same root.
To expel a foreigner from a country, typically on the grounds of illegal status or for having committed a crime; (archaic) to conduct or behave oneself.
From Old French 'deporter' (to divert, amuse, behave), from Latin 'dēportāre' (to carry away, transport, banish), composed of 'dē-' (away from) + 'portāre' (to carry). The PIE root is *per- (to lead, pass over). In Latin, the primary sense was carrying someone away into exile. Old French softened this to 'amuse, divert' (carry away from boredom), but English
The word 'deportment' (how one carries oneself, one's behavior and manners) and 'deportation' (being carried away from a country) come from the same Latin verb. The split happened in Old French, where 'se deporter' meant 'to carry oneself' — hence 'deportment' as bearing and conduct. The English word 'sport' is also a descendant: Old French 'desporter' (to carry away, to amuse) was shortened to 'sport' — amusement that carries you away from work.