The phrase "gravely undermine" is correct and usable in written English.
You can use this phrase to convey a sense of serious damage or danger. For example, "The new laws will gravely undermine public safety".
They say Mr. Oxley's proposals gravely undermine protections for insurance customers.
In a May 25 letter, they said they had uncovered information that would "gravely undermine the credibility" of the accuser.
They will be listening to testimony that appears to gravely undermine the official justification for going to war.
He has hired private detectives as well as prominent defense lawyers who have said in court papers that they have "substantial information" that could "gravely undermine her credibility".
And Cardinal Vincent Nichols, the Roman Catholic archbishop of Westminster, has condemned the bill as legalising "assisted killing" which would "gravely undermine" the value of human life.
These developments gravely undermine the peace agreements in place and the efforts of the international community to consolidate peace in the Central African Republic.
At those levels, there is intense debate about whether American security would be gravely undermined.
The President's bumbling has gravely undermined the credibility of his Secretary of State.
What was conceived as a strong constitutional base for national unity, through a unitary judicial system, would be gravely undermined.
Murdoch and Blair remain on friendly terms, even though Blair's support for the war in Iraq and for President George Bush have gravely undermined his popularity.
This full-throated denunciation is so often inaccurate that, even if the companies are as powerfully diabolic as Juhasz claims, she ends up gravely undermining her point.
