What you are doing is putting the brakes on. What we say is brake eg When you do an emergency stop, you brake hard enough to stop quickly but no so hard that you skid. Colloquially this is known as slamming the brakes on.
We would not normally refer to a passenger in a car as "my copilot".
Are you flying an aeroplane?
Alternatively, are you driving in a car rally?
Assuming the latter, the conversation would probably be something like:
Copilot: "Would you mind slowing down a little here?"
Claude: "Of course, my friend, I shall apply the brakes imminently."
- or to be more realistic:
Copilot: "SLOW DOWN!!"
In practice, I can't imagine the driver saying much beyond OK in this context. Either that or an explanation as to why she has no intention of slowing down at this point because she is already ten seconds behind the leaders.
Edit: Sorry Claude - I posted without seeing your explanation.
... I'll step on the brakes. I understand that this sounds odd, because there is only one pedal to step on, yet it is the common way to say it. It probably comes from apply the brakes, since there are four, but nobody actually says apply the brakes. You'd read it in a manual.