It actually means literally a “sauce spoiler.”
The term meant at first a bad cook, then overtime, came to mean young, menial kitchen help, as in a scullery maid or a scullion (a kitchen boy), or a boy employed to turn the spit.
Literature & Lore
Georges Méliès, an early French film maker, made a 1-minute film called La Vengeance du gâte-sauce” (The Revenge of the Bad Cook) in 1900. It takes place in a kitchen, where the cook is trying to snog the maid. When the house-owner is heard approaching, the maid drops the plate she is holding and runs away, while the cook hides in a large cupboard piece of furniture. The owner finds the cook there and as the cook tries to come out of the cupboard, the owner squeezes the door closed and accidentally cuts the cook’s head off. He puts the head on the table until it starts terrifying him by leering at him, then he throws it into the cupboard. A moment later, the cook walks out, whole again, and tears his bosses head off. Meant to be comic.
From the French verb “gâter”, meaning “to spoil.”