Frames have a minimum insert requirement - 100mm-120mm for carbon is not uncommon. Seat posts also have a minimum, which is usually marked on the post - typically 75-100mm. Both these limits should be adhered to. A long seat post may be too long to lower the seat to the correct position. The difference between the minimum insertion and maximum will vary based on the frame, however it can be quite a small range especially on some more exotic shaped frames (e.g. Softtail MTB's)
The only advantage of going to the minimum insertion is weight savings. However going short adds stress to the seat tube.
The only significant disadvantages of a longer post is weight.
What length post to use between these minimum and maximum insertion depths will depend largely on your own preference for weight saving over strength and your weight and riding style. My lightweight XC MTB has 100mm inserted (100mm minimum), but I am 66kg, and don't do jumps. If I was 120kg and loved big air, it would have 200mm or more.
You can cut the end of the current seat post. Find the minimum insert for the frame and post, measure that much below the current posts location in the seat tube and rip into it with a hacksaw. When I have done this in the past, I also sand off the minimum insertion mark put a new one on the post.