Trump, who has called Ms Harris and Mr Walz a “radical Left duo”, said he would be focusing on the Midwestern governor’s support for the trans community on the campaign trail.
“This is a ticket that would want this country to go communist immediately – if not sooner,” Trump told Fox News’s morning show Fox & Friends on Wednesday.
“He’s very heavy into transgender. Anything transgender he thinks is great.”
Trump, 78, added: “He’s not where the country is on anything.”
Trump campaign insiders have suggested they were relieved by Ms Harris’s decision to opt for Mr Walz as her running mate over her other short-listed candidate, the Pennsylvania governor Josh Shapiro.
Republican strategists believed Mr Shapiro, 51, a rising Democratic talent, could have delivered his home state for his party, which is considered critical to winning November’s election.
Mr Shapiro faced an intensive lobbying campaign from progressives over his staunch support for Israel.
His snub in the selection process has triggered accusations of anti-Semitism from Republicans.
Trump said the snub was “very insulting to Jewish people”, but added he “couldn’t be more thrilled” Ms Harris went with Mr Walz, casting him as an easier opponent to defeat.
The former president also signalled he was prepared to debate with Ms Harris “in the pretty near future”, despite backing out of a scheduled appearance against his Democratic opponent on ABC News on Sept 10.
Trump suggested an alternative head-to-head with Ms Harris on Fox News on Sept 4, prompting her campaign team to accuse him of “running scared”.
Speaking to Fox on Wednesday, Trump teased the prospect of an announcement on a new debate “fairly soon”.
He separately suggested Joe Biden could crash the Democratic national convention later this month to try to “take back the nomination” after it was “stolen” from him by Ms Harris, former president Barack Obama and “others on the Lunatic Left”.
“He feels that he made a historically tragic mistake by handing over the US presidency, a COUP, to the people in the world he most hates, and he wants it back, NOW!!!,” Trump said in a social media post.