I want a bigger size chin implant. If I get a large one, will the scar move up? Will they have to make a second cut?

Usually the same incision without making it bigger is possible for implant exchange for a larger chin implant. It will be in the same position, (near the crease)

Typically, moving from a medium to a large chin implant, the previous incision would be used. If that scar was at all widened it could be removed at the time of surgery. A larger implant will move that scar forward to some degree but this is usually negligible as long as the incision was properly placed the first time. Stephen Weber MD, FACSDenver Facial Plastic Surgeon

If you had a submental approach the same incision will likely be utilised - your surgeon will likely excise it at the time. It is unlikely that there would be any significant change in the position of the scar if it was made in an appropriate position. You should also consider other chin augmentation options including an osseous genioplasty. RegardsDr Guy Watts

I am assuming that your chin implant was placed through an incision underneath your chin.  If you were going to change that implant to a larger size, the same incision should be able to be used.  So, the scar should remain the same and at the same location in most cases.  

 It is possible to up-size a chin implant. This can be performed under local anesthesia. The  previous incision is cut out and the old implant is removed as well.  Once the old implant has been removed, the pocket is made bigger and the new implant introduced into the new expanded pocket. For many examples of chin implants, please see the link below

The same scar is typically used to replace a chin implant.  The "pocket" under the skin will need to be widened to accommodate the larger implant, but the implant can usually be placed via the same incision.  Your doctor can give you specific advice and recommendations after seeing you.

Dear Duong, When doing revision chin augmentation and moving to a larger implant the surgeon would typically go through the old incision. Assuming this incision was placed properly it should not move up and be more noticeable then the primary one. Best regards, Michael V. Elam, M.D.

Yes, your request is possible.  The surgeon will go through the old scar, so there will only be one scar.  The old scar will not be there, so it can not move up.  A photo would have helped to be sure you are a candidate for a large implant.