At the Unite Scotland union's conference in Clydebank, Ms Dugdale accused the Scottish government of making cuts to schools and social care.
Also speaking, UK Labour party leader Jeremy Corbyn pledged that a future Labour government would repeal the Trade Union Bill.
First Minister Nicola Sturgeon will be making a speech to delegates on Sunday.
Ms Dugdale told the conference Scotland could not be a "fairer, more prosperous country" while councils were being "starved of the resources they need".
She said: "We cannot build a better life for those children when their parents are amongst the thousands of local government workers who have lost their jobs or the 15,000 more who Cosla say could go as a result of John Swinney's Â£500m cut to our councils.
"We should be cutting the gap between the richest and the rest, not the budget for our schools and the workers from our services.
"I am calling on all trade unionists to join Scottish Labour and speak with one voice to say these SNP cuts to local councils responsible for our schools and social care just aren't acceptable."
Mr Corbyn, who was delayed arriving in Scotland because of bad weather, said Labour was setting up a commission on workplace rights to be led by the Shadow Minister for Trade Unions, and former president of the National Union of Mineworkers, Ian Lavery MP.
The Labour leader said: "Not only will we repeal the Trade Union Bill when we get back in 2020 we will extend people's rights in the workplace - and give employees a real voice in the organisations they work for.
"That means new trade union freedoms and collective bargaining rights of course because it is only through collective representation that workers have the voice and the strength to reverse the race to the bottom in pay and conditions."
Mr Corbyn said he was proud to be a member of a trade union and the unions would be "central to everything we do".
An SNP spokeswoman said: "Kezia Dugdale should ask Jeremy Corbyn to support the SNP's calls for trade union laws to be devolved as Labour voted to leave these powers in David Cameron's hands, instead of allowing the Scottish Parliament to take a new and better approach, giving him carte blanche to undermine unions in Scotland."
Among other issues being debated at the conference are debt, the oil industry, fracking and devolution.
Meanwhile, Unite's general Secretary Len McCluskey is set to urge Labour to apologise for "betraying" Scotland to stem the drift towards the SNP which already claims two thirds of Unite's Scottish membership.
Mr McCluskey will remind Scottish members that Unite is a Labour affiliated union and urge them to come back to Labour, in a speech on Sunday.
He said: "The ideology of New Labour effectively alienated large swathes of the Scottish working class, which manifested itself quite dramatically last May.
"Kezia has to effectively say: 'Labour is under new management, we apologise for betraying you, and we will start from scratch to try and build that trust up'."
Scottish Labour leader Kezia Dugdale has called on trade unionists to "unite against SNP cuts to local councils".