Could applying a tourniquet cause harm?

Yes, it can cause damage, if the tourniquet in use is of poor quality, too narrow or too weak, has no tightening mechanism or in those cases, when the tourniquet is not sufficiently tightened and stops venous blood flow only. In latter cases, the blood brought by the arteries cannot return back through the veins, causing more bleeding. Tight bandaging of the wound, which seemingly ceases the bleeding, leads to further swelling and internal tissue damage. It is also life threatening to apply the tourniquet too late, or if it is briefly released or completely removed by non-medical personnel, leading to bleeding to death.