No, HCG is pretty useless for cutting. It may increase testosterone but not to any extent which would be useful/noticeable for cutting.
The HCG diet, is a scam. It consists of you eating 500 calories a day and taking HCG. The HCG is irrelevant to losing weight if you are only eating 500 calories a day. Of course 500 calories a day will lose you weight (consisting of muscle and fat) but you cant keep that level of calories up for the rest of your life and as soon as you go back to your usual levels you will pile the fat back on quicker than ever as your body attempts to super compensate for you starving it.
There is only one type of HCG. Human Chorionic Gonadotropin. It can be created in different ways (via extraction from urine of pregnant women) or synthesised in a lab. They are identical whichever method is used to create it. You may see some HCG for sale which taken orally or nasally. These are a waste of time and useless as the delicate HCG glycoprotein is destroyed by these methods of ingestion before it gets near your bloodstream. The only way to take HCG is by injection.