We can localise cancer cells in the body. We can manufacture materials thin and hard enough to penetrate the body without harming it. So what stops us from creating an automated surgery where the patient lies down for some time whilst a machine locates cancerous cells and, using micro tubes, kills them one by one?
Actually we aren't that good at localizing cancer cells. There need to be around 100,000 cancer cells at a single location for the cancer to be visible on fMRI.
If you want to treat a cancer via chemotherapy it's good to be able to see the cancer. It allows you to see whether the drug you are giving works.
When dealing with a metastasized cancer where you don't think you know every location in which cancer is hiding it therefore often makes sense to avoid to take out everything you can see via surgery.
I'm assuming you are not talking about a single solid tumor, but rather one where the tumor is loose and is distributed throughout the tissue, or has metastasized
I guess the answer is you could, but it would be one amazing machine. This robot would have to examine each individual cell and destroy it based on what you could sense about the surface properties. Identifying cancer cells on the basis of the proteins and glycosyl (carbohydrate) molecules on the cell surface is not embodied in a reliable way in a touch sensor. Cancer can manifest lots of such patterns and it could quite easily be that if you looked at healthy cells, they look very similar. Cancer cells don't have an obvious sign they are always holding out saying 'im cancer'...
Then there is the structure of tumors. For instance glioma is one of the most difficult brain cancers you can have. The glioma cells push out axons - they can be quite long. Its hard to imagine a robot that could find that in a brain without tearing up all the neural connections. In prostate cancers - one of the most common cancers in men, the cells are embedded in the tissue surrounded by necessary and healthy cells.
This is why chemicals and nano structures are the most commonly pursued means of combating cancer; they can enter into cells that are embedded in solid organs. Differentiating the cancer cells from other sorts of cells in vivo is a pretty hard problem - some antibodies are given as a possible help there, but they are not reliable.
This blog post is a pretty up to date summary of where we are
It’s not a question of materials. After all, we have the materials to build flying cars – so why are there no flying cars? The problem is reliably locating, recognising and selectively killing tumour cells.
“one by one” … for billions of cells? Even ignoring all the other technical problems already alluded to in other answers, this is simply a problem of insurmountable scale. In order to do this efficiently we’d need in the order of millions tiny robots.
Either way, creating appropriate robots isn’t something we can do today, and even if we can someday do it, it will be easier (and much, much cheaper) to just bio-engineer a bacterium which detects and kills tumour cells. While neither nanobots nor bio-engineered cancer killers are reality today, the bio-engineering approach is much easier, and much closer to realisation than the nanobot approach.