Botulinum Toxin is the most acutely toxic substance we have ever found, but it is used routinely for medical and cosmetic procedures, just in incredibly low doses. But it had to be demonstrated safe (i.e noncarcinogenic) at those doses (a number of deaths have been attributed to botulinum toxin use, due to allergic reactions or inadvertent spread of toxin to sensitive areas). Of course, as it is used more, the subtle effects become more apparent (things like emotional damping, possibly due to reduced feedback from paralysed facial muscles when botox is used cosmetically).
But if there is no good reason to investigate (i.e no theraputic value) a highly toxic substance that generally causes death will not be specifically investigated for carcinogenicity. It is only where there is a sufficient level of non-lethal exposure and enough statistical evidence to warrant a connection with cancer that would trigger such a specific investigation.
There are tests that measure the potential for a chemical to cause mutations in bacteria (e.g. the Ames test). To be precise, that determines whether the compound is a mutagen, and not whether it is a carcinogen. The vast majority of carcinogens are mutagens, though the converse isn’t true. I’m not entirely sure why this is , but I suppose that human cells might be able to repair or resist certain types of mutagens that have an effect in bacteria.
Anyways, that’s why a lot of things are labelled as “possible carcinogens”. Using a test like the Ames test, some chemical was found to act as a mutagen, but otherwise there is no direct evidence that it causes cancer.
Think I’m right in saying that the list of confirmed carcinogens in humans is pretty short, because obv you can’t test suspect carcinogens on humans. So you’re relying on data from things like industrial accidents / exposures, or historic use of a material that was once thought safe etc, where groups of people have ingested a substance and then developed cancer.
The list of substances that are suspected to cause cancer and almost certainly do is no doubt pretty long. Because you can test for mutagenicity like lazybratsche says, test for cancer in animals, or just assess its structure on chemical and biochemical principles (e.g. any reactive alkylating agent is a safe bet for a carcinogen).