How do you thicken Chinese sweet and sour sauce without using any starch?

You can thicken the Chinese Sweet & Sour sauce by simmering and reducing it.

Simmering a sauce to reduce it will thicken it but it will become very strong and syrupy which I don't think you want.

There really isn't a replacement for using a slurry of some sort of starch dissolved in little water.

Hmm... all of the thickeners are starches: arrowroot, cornstarch, tapioca starch, flour. You can thicken the sauce by reducing it or add pureed vegetables such as carrots. You could also try almond or coconut flour which are lower in carbs.

You can do any of the suggestions, but I'll tell you that part of Chinese sweet and sour is the "mouthfeel", and that comes from cornstarch, usually.

Shitake mushroom, potatoes, taro, yam etc if added to the sauce will thicken it

You could use arrowroot, tapioca powder or flour.