The Shadow Chancellor’s comments come ahead of his visit to Midlothian, Clackmannanshire and Glenrothes on Saturday to speak with activists and councillors.
He also hit out at the SNP over its budget and claimed “only Labour” can provide investment the country “desperately needs”.
Mr McDonnell said: “Communities across Scotland have been suffering for too long under the impact of austerity.
“The SNP could have adopted Scottish Labour’s plans to halt austerity in Scotland, but they chose instead to pass a budget that doesn’t deliver a pay rise for the local government workforce and will leave lifeline local services under pressure.
“Scottish Labour offered a budget for real change for Scotland that would have delivered a near £1 billion stimulus for the Scottish economy, secured an additional £100 million for the NHS in Scotland and a fully funded pay rise for all public sector workers.
“The SNP should stop playing politics with people’s lives and listen to Richard Leonard’s plans to truly end austerity in Scotland.
“The truth is that only Labour at Holyrood and Westminster can provide the investment that the NHS, councils, higher education and all other public services in Scotland desperately need.”
The Scottish Government’s budget for next year passed its final vote at Holyrood on Wednesday by 70 votes to 56.
Finance Secretary Derek Mackay said the budget would bring about £1.2 billion of additional spending to invest “in a fairer Scotland”.
The minority SNP government made a deal with the Scottish Greens last month to ensure its proposals were passed.
It includes major changes to Scotland’s income tax rates and bands, which will see higher earners pay more and lower earners pay less.
Opposition parties argued the plans were not ambitious enough, with Labour calling for greater tax rises for top earners.
SNP MSP Christine Grahame said: “This week Scottish Labour voted with the Tories against a Budget that brings an additional £400 million to NHS Scotland, commits £100 million to mitigating welfare cuts, and delivers a pay rise for public sector workers, which Labour in Wales have refused to back.
“It’s completely unjustifiable.
“Here in Midlothian yet again with the help of the Tories, Labour are cutting learning support and teacher numbers, increasing the cost of school meals, introducing charges for musical tuition, and closing football pitches.
“Labour or Tory, Tory or Labour - what’s the difference?”