That's not really what a threat to sever relations means. It would be talking about not having any formal diplomatic relations. All of the embassies and consulates each has in the other country would be closed. Diplomatic representatives would be required to exit the respective countries. The Russian foreign ministry would not communicate directly with the Canadian foreign ministry; they'd find some sort of proxy country to act for them.

The US doesn't have diplomatic relations with a few countries like North Korea. We entrust, as I recall, Sweden to speak for us in North Korea.

googles

Yeah.

https://www.state.gov/u-s-relations-with-north-korea/

The United States and the DPRK do not have diplomatic relations. The Swedish Embassy in the DPRK is the U.S. protecting power and provides limited consular services to U.S. citizens. The DPRK has no embassy in Washington, DC, but it is represented in the United States through its mission to the United Nations in New York.

That being said, Russia issues threats like crazy and doesn't follow through on a lot of them, so I don't know how seriously one should take this.