Is the Nipple Always Removed During Nipple Surgery?

The nipple is rarely removed for most nipple surgery. Further details, your photographs, and  an examination  would be required for the best advice.

In most instances the nipple is left attached to the breast tissue and gland and the skin is moved around the nipple or the noipple is rearranged within the "skin envelope."

The nipple is seldom removed before any surgery, including breast lift, reduction and augmentation.
In a lift or a reduction the nipple is left intact to the underlying breast tissue and it is kept on this platform so that it can survive. The the surrounding skin and breast tissue is contoured and then the area is closed.
Only in very very large reductions is the nipple removed and then placed back on. Even this has become very pase' as there are better techniques to allow the nipple to remain attached even in very large breast reductions.
Hope that helps.

The nipple/areolar complex is rarely 'removed' during breast reduction or lift. With current techniques for breast reduction and lift, the nipple areolar complex is kept attached to the underlying breast tissue to provide blood supply. The surrounding skin is removed and tailored. Rarely would a 'free' nipple graft be performed, perhaps in a very large, pendulous reduction or in a situation where the blood supply is compromised.

With modern breast lifts and reductions, the nipple is almost never removed.
Rather, it is repositioned, still attached to the tissues underneath it that supply it with blood supply and nerve supply.
Removing of the nipple has become more an emergency maneuver if blood supply becomes compromised during the surgery, occasionally in extreme breast reductions.