Can I widen my mouth? The measurement of my mouth scores too narrow for my face. (Photos)

You would get a nice improvement with lip fillers. These fillers, (Volbella, Restylane, Juvederm) are good to create a symmetrical lip while making it appear wider. Nova threads can be used to improve lift and shape. Implants or fat are alternatives. Technique will be important here, so you'll want to see someone meticulous. I recommend getting a formal evaluation with a facial sculpting expert. Best, Dr. Emer

Lip augmentations with fillers is a great option to improve the fullness, suppleness and symmetry of the lips which can make the mouth appear wider. Results can be very natural-looking and will feel very natural. I prefer to use a micro cannula to inject the lips to prevent bruising. Look for a cosmetic dermatologist or plastic surgeon who is an expert in fillers to discuss your desired results and concerns. 
I hope this helps.

Beauty is in your heart. When you feel it, the world sees it. Your face looks sad due to how you feel about yourself.  There is nothing wrong with your mouth or your interpulliary distance. Cutting the corners of your mouth will permanently disfigure you.  The scary thing is that if you knock on enough doors, someone will do this for you. Looking at your pictures, the most evident issue is that you have upper eyelid ptosis and a right compensatory eyebrow elevation. This can be corrected with ptosis surgery and anchor blepharoplasty.  This will brighten your face. 

Thank you for your photo. You have nice features and proportions including your lips. Releasing the corners of your mouth will not be a good idea and will disrupt your appearance as well as the function of the oral sphincter which controls your mouth. You may be better served with injectable fillers to increase the length of your lips and improve their width relative to your lower face. Hope this helps!Johnson C. Lee, MD
Board-Certified Plastic Surgeon
IG: @drjohnsonlee

I think you have beautiful lips and I would not do much there.  With regards to your lower face, I would consider Botox or Dysport injection to the masseters which would slim your lower face and improve face proportions. 

Mouth widening is done by relocation of the lateral commissures through triangular skin excision and vermilion advancement. The keys are removing a wedge of the orbicularis muscle and keeping the scar at the vermilion-cutaneous border.

you would be deformed forever if you "snipped" a little from the corners of your mouth. Stop looking at your mirror........this will not end well.