The announcement, made by Conservative ministers on Tuesday, confirmed the removal of the Golborne Link from HS2.
The 13-mile link would have helped connect high speed trains from the north west of England to Glasgow, creating more capacity and cutting journey times.
HS2 minister Andrew Stephenson said the UK Government would now explore how HS2 trains could best get to and from Scotland.
However, the move has been criticised by the SNP, which suggested Mr Johnson timed the scrapping 30 minutes before the announcement of the outcome of his confidence vote to ensure it would “fall off the radar”.
Gavin Newlands, the SNP's shadow transport secretary, said: "This sleekit move sums up Boris Johnson’s tenure as Prime Minister – cowardly and shameful.
“His decision to announce this crucial cut on the same day as his vote of no confidence – knowing full well it would fall off the radar – is despicable.
"The original investment would have drastically improved Scotland’s rail links with the north west of England, but yet again this Westminster Government is tearing it apart.”
Railway industry bodies have also been critical of the move.
Darren Caplan, chief executive of the Railway Industry Association, told BBC Good Morning Scotland on Wednesday: "The way it’s come out is a pretty negative start to it all.
"The Government has to answer on it’s timing of this and it’s not a very good way to announce a £3bn cut to a scheme.
“The danger in this is there is not even a solution on the table. We need to know what the plans are.
"We need to build on the capacity of rail for the next 20 years and that means doing the work now.
"By cutting the schemes now, you don’t just make it harder for us today, you make it harder for the next 20 years when we are trying to build a world-class rail network.”
Mr Caplan said the lack of links would create “bottlenecks north of Crewe and Preston” and lead to slower and more delayed journeys.
The Golborne Link would have branched off the high-speed line between Crewe and Manchester and cut through Cheshire and Trafford to join the West Coast Mainline south of Wigan.
Mr Newlands went on to say nothing Mr Johnson says can be trusted. “Whether it’s promising to improve rail links in Scotland, building a multi-billion-pound bridge between Scotland and Northern Ireland, or investing £1bn in carbon capture in the north east – nothing that comes out of Boris Johnson’s mouth can be trusted,” he said.
“Time and time again, the SNP Scottish Government has been forced to work with one hand tied behinds its back, while the UK Tory government impose cuts and scrap pledges. This has to end."
The announcement comes six months after the Government dropped its plan to extend HS2 to Leeds.
Construction on the Golborne Link had been due to start in the early 2030s, with the connection expected to open towards the end of that decade or in the early 2040s.