Do you want to cut the seat tube or the seatpost?

Have you considered being fit on a fit bike?

What is your inseam length?

I am an almost an inch taller than you at 5'6". My inseam is 31" and I fit fine on the 51cm IA16 and as far as I know nothing was cut. In fact during my initial first ride the seat post slipped by an inch or more so it appeared that the saddle could have been dropped even more. I've had some taller shop mechanics make comments on my inseam length though when they tested my bike after tuning.

If you are not sure maybe buy the bike and then go to a reputable fitter before anything is cut. That was my plan, but somehow we lucked out and got the bike dialed in very good just off the rough build and rough fitting.

You should never buy a bike first.

You must have a short inseam if the 51 seat does not get low enough. I'm not much taller than you and I could fit on a 51 or 54. The general advice for the IA is to get the largest frame size that fits you. For my height the felt website says I could fit a 48, 51 or 54. After a proper bike fit I went with the 54.

I personally havent heard of anyone cutting the felt seat tube, or the seat post. I would get a second opinion before purchasing the bike. I would get a proper bike fit on a fit bike to figure out what size you need before purchasing a bike. The cost of a good fit is a small price to pay to make sure you arent wasting you money on the wrong bike.

If you dont know of any good fitters in your area slowtwitch has a directory of fitters all over the world. If you provide your location people may have suggestions of good fitters in the area.

Thank you,
my inseam is 30.5.