How to delete part of the mesh with smooth fading?
Is there a way to remove a part of the mesh without having a sharp break at the edge of the removed area? In other words, is it possible to make smooth fade?
I need this to blend two hairstyles together.

Comments
Not by mesh deletion, no - using an opacity map (well, for hair probably editing the existing opacity map, directly or by adding another image on top in Multiply mode through the Layered Image Editor) would let you fade it out. Strand-based hair is trickier, though there are control maps which could be edited.
I assume it is a hair that uses hair cards.
If you remove (or hide) the geometry, the geometry will not be visible, but no sort of fading.
You might be able to do it, with cutout oppacity. In hair with haircards, they usually use an UV, where each card lays up-down in the UV layout. If the area where you want to make adjustments, it would probably be better, as you else would adjust all the hair. (you could create a new surface for the hair in question).
Then in the image in the cutout oppacity, make a gradient, where it is black at the bottom, and white at the top. Exactly where the gradient should go depends on how much you want to remove. Black means invisible, white visible.
You can do it as an image overlay, or in a seperate image editor.