Your Green Card status will not be revoked at the border, but you may very well be questioned about it...on either side of the border. The CBSA could also ask you how you plan to maintain both.
It is very difficult, though not impossible, for a person to maintain both GC and PR status simultaneously. The PR R.O. (Residency Obligation) is by far, much more lenient/generous than the GC requirements.
PR status-
https://www.cic.gc.ca/english/helpcentre/answer.asp?qnum=727&top=4
GC status-
https://ois.iu.edu/scholars/permanent-residence/absence.html