Fat Removal or Weight Loss? (photo)

Young patients with "fat" int the lower face and sagging looking face as well double chin could benefit from multiple plastic surgery procedures. 
"Saggy-looking face" is a sign of weak cheek bones. Therefore in this cases, it is very likely necessary to enhance the weak cheek bones with either soft tissue fillers or cheek implants. I personally like more  filler injections on the cheeks because their result are instant, are usually done in the office setting and have associated minimal downtime.
"Fat in the lower face" is usually caused by enlarged buccal fat pads ( pockets of fats in the lower anterior cheeks). Buccal fat removal is the plastic surgery procedure that permanently removes the fullness of the lower anterior cheeks 
Double chin is caused by excess of fat in the skin underneath the chin. This physical finding can be corrected with either chin liposuction or kybella injections, I personally recommend chin liposuction because the results are more drastic and the downtime is significantly lower than with kybella ( which causes at least 2 weeks of massive neck swelling -"frog-like neck")

If you lose weight via diet, exercise etc. you lose body fat overall. You cannot control where the body will lose the fat so you cannot spot reduce fat that way. The only way to spot reduce is some type of liposuction.

Given your age your posted photo looks like the buccal fat has fallen downward over the lower jaw. If you can manually manipulate this fat back into the check the best way to get rid of it is via a small incision inside the mouth. If you cannot manually raise it I do not think you will be able to get it out that way. If the cause of this facial shape is enlarged masseter muscles you have to shrink the muscle and botox is a good option.

My response to your question/post does not represent formal medical advice or constitute a doctor patient relationship. You need to consult with i.e. personally see a board certified plastic surgeon in order to receive a formal evaluation and develop a doctor patient relationship.

Always best to try weight loss before any surgery, even if a minor operation. Seek in person consults before continuing. 

Fuller faces, particularly in the lower half, are challenging to get a significant reduction. What can be changed are some fat collections which are limited as to how much can be removed. A buccal lipectomy actually only affects fullness right under the cheekbone not the whole way down to the mouth area. Small cannula liposuction can be beneficial for reduction of submental, perioral mound and lateral facial fat. A partial buccal lipectomy may also be useful. The question with these procedures is how significant a change they can create.

Considering that you are 21, and our faces can thin out and lose fat as we age; I would consider optimizing your weight first prior to proceeding with any surgical procedure that is not reversible.  Buccal fat pad excision is performed more frequently in patients undergoing upper jaw surgery were surgical elevation of the jaws may cause excessive fullness in the cheeks. It is much less frequently performed in other situations.