Trump's immigration numbers are irrelevant as the number of border crossers has doubled under Biden.

They're not irrelevant. They show that this is a problem that had already started under Trump and that his border policies were ineffective to stop the increase from getting going. It's continued to increase, but it's obvious that these flows are due to exogenous factors and not the particulars of U.S. border policy that are under the control of the President.

I'm wondering if a simple executive order could suspend the amnesty process entirely.

This has nothing to do with amnesty. The current problems are stemming from the asylum process, not amnesty.

Assuming you meant asylum rather than amnesty, the answer is no. The asylum process is a function of statute. Asylees are legally entitled under U.S. law both to request asylum and to remain in the U.S. until their application is heard. The President cannot suspend that process through executive order.