How important is GRE in Econ Phd Applications? Does GRE play as a cut-off point in one's Economics Phd application even though s/he has a strong profile including 4.0 GPA, strong recommendation letters, good SOP, and relevant research and teaching experience?
Yes, it does, at a large number of, although certainly not all, top economics departments in the United States. Indeed, they have a lot of applications to read from perfect applicants (at least on paper). Why should they give any exceptions?

But they do give exceptions. I don't know entirely your circumstances, and certainly mathematics isn't economics. But from my own experiences, having 1. written letters for people with bad mathematics subject test GRE scores and 2. being swayed when I've been on committee to admit people with bad mathematics subject test GRE scores, I would encourage at least one of your letter writers to contact someone at each of the schools you applied to to keep a lookout for your application/not throw it out immediately presuming a GRE cutoff, especially if other parts of your application are quite competitive for the schools you are applying/have applied to.