I want you to wipe my tears.

Literal

Tears [object-を] wipe want [favor-てほしい].

~てほしい is the desiderative-for-another pattern: 'want someone else to X.' Attached to the て-form of 拭く ('to wipe'), it means 'want (you) to wipe.' The subject of the wanted action is typically marked with に in the full form, but here omitted. Emotional, intimate register.