Is it common to cut the wings of a chin implant?

If your face is narrow, the lateral wings help improve this. However, I agree that in many patients, the lateral wings masculinize the face and, in addition, amplify asymmetries that commonly exist along the lateral chin. However, when the lateral wings are trimmed off, the implant becomes unstable and can flip over or tilt over. To prevent this, I prefer fixation with a small screw. I strongly prefer a Medpor implant, which is less slippery than silicone, without the lateral wings and fixate the implant with screws.

It is possible to trim the wings or sides of a chin implant if they extend too far for your purposes. The wings taper quite a bit toward the sides so they don't necessarily create a lot of volume further out, but that depends a lot on what size implant is used.I don't find that implants commonly have to be trimmed, but it is certainly an option.

There are chin implants that do not have wings, so is it not common to cut the wings off of the implant. If you feel an implant with wings is not for you, I would consider one of the chin implants without wings.  

Fortunately, chin Implants come in many shapes and sizes.  Therefore, discuss your desires with your surgeon so the correct chin implant will be available at your surgery.

 Hi, I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  Non smiling photos of your face from the front and side would help in the evaluation.   As described below, chin implants provide "forward" projection to correct a weak chin.  If, your chin is not weak, then there's really no reason to have a chin implant.  If you do have a weak chin, the EAC (extended anatomical chin implant) style implant in my humble opinion provides the most "natural" augmentation mainly because their wings provide a natural taper on the each side of the implant.  Should the wings be removed, or an implant used without wings, this approximates the old curvilinear style chin implant.  That style implant fell out of favor in the 1980's because it created a exaggerated front augmentation (without a natural taper on the sides) resulting in what was called a "Pharoah's chin".  This, in my opinion, would be the primary reason for not cutting off the wings of an EAC chin implant. When the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  
 Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  
 I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty (requires extensive tissue dissection, bone cuts and placement of metal screws and plates to secure the cut segments of bone).  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.    
Hope this helps.