Separate, part, divide, sever, sunder, divorce can all mean to become or cause to become disunited or disjoined.
Separate implies a putting or keeping apart; it may suggest a scattering or dispersion of units or a removal of one from the other or the presence of an intervening thing or things.
Part usually suggests the separation of two persons or things in close union or association; often also it suggests a complete or final separation (as by death or violence).
Divide commonly stresses the idea of parts, groups, or sections resulting from literal or figurative cutting, breaking, or branching.
Divide often, in addition, carries an implication of apportioning, distributing, or sharing.
Often divide is used in place of separate, especially when mutual antagonism or wide separation is connoted.
Sever adds the implication of violence by or as if by cutting and frequently applies to the separation of a part from the whole or of persons or things that are joined in affection, close affinity, or natural association.
Sunder often implies a violent rending or wrenching apart.
Divorce implies the separation of two or more things so closely associated that they interact upon each other or work well only in union with each other.
Divorce can specifically refer to the legal dissolution of a marriage, a use in which it contrasts with separate which implies a mutually agreed ending of cohabitation without actual legal termination of the marital state.