Tig Notaro is in the prime of her career. A documentary about her life, called Tig, premiered at Sundance; her autobiography is out next year; she’s a regular on This American Life; and her comic collaborators include Sarah Silverman and Amy Schumer. Her personal life, though, has been much tougher. Notaro is only 43 but in one four-month period three years ago had to deal with bereavement, the breakup of a relationship and a life-threatening illness.

The Guardian met her at SXSW in a cafe in Austin, Texas, where she’s showing another film that will be broadcast as a TV special on Showtime. Knock Knock It’s Tig Notaro charts a recent tour in which she performed in fans’ houses all over America, from Chicago to Pluto, Mississippi, her home state. It’s striking how at ease she is in front of any audience, and how much love she gets back, particularly when doing an impression of a clown’s honking horn at extraordinary (some would say infuriating) length. She has an almost abstract comedic style that likes to play with people’s expectations, for instance moving the microphone stand into a different room, and then laboriously bringing it back again.

OK, perhaps you have to see it for yourself.

Going to people’s homes “is just silly, a fun way to do standup”, she says. “It’s a cool way to see towns and meet interesting, weird people. Even the disasters are fun.

“One year I was touring with my friend Steve Agee, from the Sarah Silverman Program; we were performing in a backyard in Eugene, Oregon. Steve used the word fag, calling himself that, and it upset someone on the other side of the fence; he jumped the fence and rushed Steve. It was a really funny moment.”

The film also has more reflective stretches between Notaro and her tourmate, comic Jon Dore. As they drive through America, the conversation turns to matters of life and death. In 2012 Notaro’s mother died suddenly in an accident; a love affair came to an end; she had pneumonia and an intestinal illness, C diff, which made her lose so much weight she was “skeletal”. Then Notaro was diagnosed with stage two invasive breast cancer.

How she dealt with this is now the stuff of comedy legend. Three days after she was diagnosed, Notaro went onstage at the Largo club in LA and casually announced to the audience: “Hello. Good evening, hello. I have cancer.” What followed was a half-hour of comedy so raw and emotionally charged that it attained instant classic status – and was fortunately captured on tape, released under the title Live (to rhyme with give).

It seemed like a performance whose intensity could never be matched. Then last November, at a gig in New York, Notaro caused another sensation.

In the period between the two performances she had recovered from cancer, her treatment requiring a double masectomy. Notaro had elected not to have reconstructive surgery. During the New York gig, she tore off her shirt, Superman-style, and performed topless.

“Oh, word got round?” she asks drily. “After surgery I was very uncomfortable with my body. I was bruised and swollen and had scars or stitches. It was a hard reality to adjust to, and then I had this idea: ‘Oh my God, what if you walked onstage topless?’ I thought that was so funny.” Notaro went off the idea as she healed, but returned to it while writing her show. She canvassed the opinion of 10 friends, one of whom said it would come across as a stunt.

“I said it is a stunt, 100%,” says Notaro. “I want people to talk about body issues, my comedy, cancer. Cancer’s a big deal, but when your skin heals, that’s good news.”

On the night, Notaro did her cancer material – “which is only seven minutes” – took her shirt off and then stayed topless while she did the rest of her routine. “It was exhilarating, the crowd were going nuts,” she says. “Everyone that I talked to afterwards was saying that their head exploded when my shirt came off and then 10 seconds later they didn’t even think about it. That was my whole point.”

Notaro says in the film that she has been back from the brink of death. It contains a sequence in which she and Dore visit a stonemason who makes gravestones, one of which they buy for Notaro. It’s simultaneously moving, weird and funny, as they explore the parameters of grieving and mortality in the light of Notaro’s illness – though this is unspoken.

Was it upsetting to film? “No, it felt just utterly silly.” During her worst times, the only point at which Notaro says she lost her sense of humour was when she had C diff; at that point she could see herself deteriorating, whereas she couldn’t outwardly tell that she had cancer.

In conversation, Notaro is matter-of-fact and wry, but speaking to her is an emotional experience. In the Showtime film, she is buttonholed by a woman at one of the shows who says that she was diagnosed with cancer at around the same time, and that she was rooting for Notaro to pull through. It’s a reaction she gets a lot – at least one person per show, she says – and one that she feels lucky to provoke.

“I used to be a very private person,” she says. “It was so out of character for me to do that show at Largo. I had no idea it was going to go viral and that it was going to change my life. Everything busted wide open for me. People have responded to my stories so well. They come up after a show and say things like ‘Your album really helped me’ or ‘I have stage four cancer, I’m terminally ill’. Somebody told me it gave them the courage to die.”

Such intense exchanges, says Notaro, stoke her awareness of and gratitude for life. “You can think you’re living in the moment and you’re thankful, but when somebody comes face to face with you and says ‘I just lost my child’ or ‘I have months to live, and thank you’ ... I’m of course sad for them, but I’m thankful that I gave them a gift and they’re giving me a gift. I think I was a compassionate person before all this, but I can’t imagine going through what I went through and going ‘Oh, well that was a tough time’ [she mimes brushing down her jacket] and then just moving on. I feel very compelled, like I have a purpose more than ever.”

That compulsion is not just career-based – how could it be? Notaro says her illness starkly revealed the aspects of life that are truly important. She is engaged to her girlfriend, and the pair plan to have children next year. “It’s a weird place to be in because my dreams in life have surpassed what I could have ever imagined,” she says. “I just hope I can continue to write stand-up, but I would say my big dream is to build an amazing family. It’s so boring and cheesy but that’s my focus.”