I would understand it that - "To spare the lovely day your ****" means to cease troubling ("spare") the day with the long agony of wishing for her, and instead go and bed her, so that the wishing agony of Faust, and the devil's efforts, can end. "betray" I would take to mean seduce in a way that society and *** will frown upon. ie betray her social/godly dignity.
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