The documentation definitely lets a lot to be desired, but doing what you want to do is definitly possible (after all the GDPR tool UI is doing it). You can take a look at the HTTP requests that are sent to the API there for inspiration.
I can find all Austrian visiters from this API:
This will give me a list like this:
And if you now want to delete this one visit
4972, you can POST to
visits[idsite]=1&visits[idvisit]=4973 as form data.
So you can also delete multiple visits with one request just like the UI tool does.