Can I deny my re-assignment orders at soldier support center for a different assignment?

You are not an interpost transfer, you are a no cost PCS. The difference being that an interpost transfer is handled internally by a 4187 from a parent unit moving you within its organization. If you have to attend the levy brief then you were placed on assignment by HRC making it a PCS. If you move from one MACOM to another, such moving from. FORSCOM to TRADIC or USASOC then that move has to be coordinated through HRC and it's a PCS.
If you requested the assignment through your reenlistment, then you can go back to your career counselor and request to have it deleted. You can't request a different unit, that's not how reassignment section works. They process what your orders say. If you want a different unit, you will have to delete your assignment and then work with your branch manager for a new assignment. No guarantees there, though.

A denial without warrant would be detrimental to your future growth. As a Soldier you have certain responsibilities, one of those is your integrity. You r-enlisted for this assignment, your gaining hitvis coontingvon you as a part of a deployable package in support of our nations bidding. Your reputation would be soiled. However, if you have a valid reason, such as a medical or the like you will be fine. Let your conscience be your guide. Thank you for your service.