In the US, and presumably elsewhere, no way. My wife tried to negotiate a higher salary in exchange for forgoing health insurance a few times, to no avail.
It won't save as much as you might expect, though, because the insurance provider also knows that the people opting out of the scheme would have (on average) cost the provider less to provide healthcare for.
I’m pretty sure it isn’t up to the company, they have to provide health insurance if certain criteria are met, it doesn’t matter if your partner already has health insurance.