Campaigning in Edinburgh today, Mr Stewart did not rule out allowing another independence vote, but he warned referendums are "a recipe for uncertainty and division for decades".
He also said Scottish Tory leader Ruth Davidson embodies the values the Conservative Party should stand for.
"I would say that [the SNP's] Alex Salmond and Nicola Sturgeon sat down and they said this was a once-in-a-generation vote and I trusted them.
"What is the purpose of drawing a border between Scotland and England?
"I'm about overcoming division, I'm not about creating more divisions. I'm trying to bring people together.
"I completely reject the idea that a so-called progressive party is trying to put up borders. It's not the solution to anything, ever."
Asked whether he would allow another independence referendum under Section 30 powers, he said: "I would argue heart and soul against it because it would break my heart. I would have no country left.
"I'm a Scot who's representing an English borders constituency. If the United Kingdom splits, then what am I? What am I representing?
"I'm completely against it, but I'm not against it in a dictatorial fashion. I would reason against it, I would make the arguments against it."
With an Article 50 extension agreed until the end of October, Mr Stewart said a citizens' assembly was "the only route through" the parliamentary deadlock.
He insisted he would be able to engage MPs in a more effective way than Theresa May to "unlock that critical 50 or 60 MPs to get [a Brexit deal] across the line."
Mr Stewart was also effusive in his praise for Ms Davidson, saying she "would be a great prime minister of the United Kingdom if, in the future, someone can persuade her to do it".
He added: "Ruth is probably the person I feel closest to in the Conservative Party. I think her way of looking at the world, her experience, her brains, her values, I think are wonderful.
"If I had a vision for the Conservative Party, it would be a Ruth Davidson party."
The leadership campaign of the self-described "unusual sort of Conservative" has been notable for his selfie-style video messages and invitations for the public to question him while travelling throughout the country.
"Listening to people and answering questions" are two of his life principles, he said - the other being walking.
Speaking about his campaign, Mr Stewart said his approach may risk failing to win the support of enough Tory MPs, but he added: "The strength is that I'm catching the public much more quickly, so at the moment I can produce quite a detailed five-and-a-half-minute talk on the problems of a no-deal Brexit and it's seen by 1.3 million people, so it's got this big reach."
Explaining what he sees as the fundamental aspect of his leadership bid, Mr Stewart said he was starting "two or three steps ahead" and added: "You've got to start with winning a general election and work backwards.
"There's a choice in this campaign: you can spend your time in Westminster trying to persuade MPs to vote for you or you can be out talking to people, trying to prove that you can win a general election. I think it's the latter that is most important."
In a polite, but barbed reference to other candidates, he said: "They're very distinguished colleagues but they're not going to win an election. That's all it comes down to.
"Whatever your admiration for these people; they're clever and principled, but they're not going to win an election."
But asked whether he would call a snap election if he becomes PM, Mr Stewart was emphatically against the idea.
"We'd be massacred," he said.
"The way to win elections is to do things. Stop talking and start doing things. Get Brexit done and then you've got to address the big challenges of our age, you've got to build two million houses, you've got to take the lead on climate change, you've got to win back the trust of people by doing stuff."
Mr Stewart said polling and focus groups indicate he is outperforming other candidates in terms of likeability, communication and the ability to convince voters to switch to the Tories.
"It's very important because we're haemorrhaging votes from both sides at the moment," he said.
"We need to get Brexit done to get those votes back, but the real challenge if we were to win an election is to get people who wouldn't traditionally vote Conservative."