Ischemia is a condition when not enough blood flows to a particular part of the body. Trauma (such as a crush injury or thermal injury/burns) to any limb or any other muscular part of the body can damage the tissues directly and indirectly. Indirect damage to the tissues can occur when the blood vessels and nerves in the area are damaged resulting in lower flow of blood. Lower blood flow can lead to hypoxia (lowered supply of oxygen). Oedema (or edema), swelling of the region due to accumulation of fluids can further compress the blood vessels which again reduces the flow of blood. As blood flow to the area is restricted, that can lead to the cell and tissue death leading to amputation of the limb.
Depending on the severity of the injury/trauma and the damage to blood vessels surgery might be an immediate option to fix the damaged blood vessels and in extreme cases, amputation might be the only option.

What happens in the body after a traumatic injury?
After an acute traumatic injury to a limb (or other part of the body), when the blood vessels are damaged, the blood starts flowing into the tissues resulting in formation of clots, poor circulation of blood and inability to maintain adequate intra-cellular water. This results in oedema (accumulation of fluids in the tissues in the area) which in-turn puts more pressure on the blood vessels causing further obstruction to blood flow. This works in cycle making the condition worse consequently leading to amputation of the limb.
How hyperbaric oxygen therapy helps in healing traumatic ischemia?
Hyperbaric Oxygen Therapy involves a person breathing nearly 100% oxygen at higher pressure, typically 2.5 to 3 times the normal atmospheric pressure. This results in filling up blood with higher amounts of oxygen getting dissolved in the blood and also in the plasma.
In case of traumatic ischemia, hyperbaric oxygen therapy helps by causing changes at cellular level. First, vasoconstriction happens in the affected area, meaning, less amount of blood and fluids will be supplied to the area. But, since the blood and plasma contains more oxygen, there will be net higher supply of oxygen to the area. (One must note that, in the air that we breathe, there is only 21% oxygen at normal atmospheric pressure whereas in HBOT there is near 100% more oxygen at nearly 3 times the atmospheric pressure.) The vasoconstriction also helps in lower accumulation of fluids (oedema). As more oxygen is supplied to the area, angiogenesis (creation of new blood vessels) takes place and also the damaged cells and tissues heal faster.
HBOT is usually not considered the first line of treatment in severe traumatic conditions. Surgical treatment including revascularization and fracture stabilization are considered first and then the treatment is complemented with HBOT. In non severe cases, HBOT may be prescribed along with conventional medicines to greatly reduce the chances of amputation.
References
https://www.ncbi.nlm.nih.gov/books/NBK537014/