Mexborough First councillor Sean Gibbons, said the budget was now 'ludicrous' after a review said it was now £22bn over budget.
He represents an area which is forecast to be the hardest hit from demolitions to make way for the line.
Transport Secretary Grant Shapps has announced the first phase of the HS2 high-speed railway between London and Birmingham will be delayed by up to five years.
That section of the line was due to open at the end of 2026, but it could now be between 2028 and 2031 before the first trains run on the route.
HS2's total cost has also risen from £62bn to between £81bn and £88bn. The second phase which passes through Mexborough has also been delayed.
The route - from Birmingham to Manchester and Leeds - was due to open in 2032-33, but that has been pushed back to 2035-2040.
The statement coming from the Transport Secretary was based on a report which concluded the new railway line ‘could not be delivered within the current budget’.
Coun Gibbons said: "The latest announcement by HS2 advising that delays to the Phase 1 and Phase 2b - now forecast as 2040 - with over £22 billion over budget is ludicrous.
"HS2 clearly do not have a clue just how much this disgraceful white elephant is going to cost the public purse.
"This has devastated the lives of hundreds of people who have fled their family homes for a unwanted vanity project which is most be scrapped entirely at the end of the year once the review is complete.
"Senior people finally need to admit the project budget, the demolitions, the lack of cost/benefit, the poor connectivity in the north and the devastation of vast amounts of countryside across the UK."
But many in the business community are still backing the project and say any delay will be a 'concern'.
Henri Murison, Director of the Northern Powerhouse Partnership said: “The timescales for HS2 need to reflect the needs here in the North, and any delay in delivering proposed infrastructure in the Northern Powerhouse will be of concern to businesses here which support it.
“The Northern Powerhouse Partnership review into HS2 will be considering this issue and the other important questions raised in full, and they will give their judgement on how the project should proceed.”