You need to remove the cassette. You will most likely not be able to simply pull the axle out from the drive side (even after you've removed the non-drive side cones) due to a dust shield on the cone under the cassette. It almost looks like your cassette may actually be a freewheel in which case all you'll need is a big 'ol wrench and a f/w tool. If its a cassette than you'll need a f/w tool and a chain whip. If the cassette/freewheel is off you'll be able to clean things much easier. It is a general rule that you remove an axle by taking off the non-drive cones or at least by only taking one side of the axle apart so as not to mess with the dish of the wheel.