While Lib Dem councillors have pledged to put local issues first, talk of the second vote - which has dominated Scottish politics in recent months - is causing anger on the doorsteps, he said.
The leader, who is confident of gains in the May 4 ballot, kicked off the party’s campaign with a visit to Scottish Grass Machinery in Inverkeithing, Fife.
He said: “The overriding message is that we are going to put mental health services and education at the top of our priority list, alongside ending the unfair council tax.
“But we are also sending a very clear message that if you want to put an end to this proposal for a second divisive independence referendum, you can vote Liberal Democrat to send that clear message.”
While the Scottish Greens have called for the council elections to be fought on local issues, and not another referendum, Mr Rennie said the constitution is being raised by voters during canvassing sessions.
“Independence is enormous,” he said.
“People are spitting mad with Nicola (Sturgeon). They cannot believe that just three years after it was settled, she’s bringing it up again.
“It’s the division in families and communities that they are really angry about.”
His comments come as the First Minister prepares to return to Holyrood to set out her next steps after her request for powers to hold another referendum was rejected by the UK Government.
“People are wanting us to get back to focusing on these local issues,” Mr Rennie said.
“They just think she (Ms Sturgeon) has lost the plot.”
The Lib Dems are the second party to publish their local elections manifesto, with pledges on improving mental health support, investing in schools and nurseries and reforms to local government funding.
Mr Rennie said some “spectacular results” in council by-elections, totalling more than 30 since the last general election, had given the party cause for optimism.
“We’re making big gains - you can see the fightback coming,” he said.
“The tide is turning, this campaign is another step in that progress, and I am confident that we will make gains.”