Assuming you plan to use the razor again in a few days and stainless steel blade, leave the blade in the razor. Some people do remove the blade and clean. Either answer is probably fine.

If planning to store the razor for an extended period or blade that may rust, remove the blade.
I am just in the habit of cleaning every razor blade, even loosening the head and running under very hot water does not take all the soapy grime off, I prefer it clean...but as I am retired I am in no rush to shave...most likely different for a lot of you guys.