Borrow a strimmer if you can.

You need to reduce the height of the grass either with a strimmer or by hand with shears, clear away the cut lengths and then mow. It is possible to do it with an electric hover mower (but not with a cylinder or non hover) but it requires skill and practice, or it burns the motor out.

How large an area is this and how high is the grass? Is it knee high? Aside from renting a rotocutter followed by a hay baler :), set your max cutting height on your mower and mow in the late afternoon when the grass is dry. Make one pass then the next day do it again only the mower blades will be set a notch lower etc until the height you desire is reached. Of course rake the cut grass clippings up between successive mowings and of course clean the underside of the mower of all grass twined around the blade shaft and caked clippings adhering to the blades and inside casing. A putty knife is good for that job..before you do this PULL the spark plug connection so you don't find yourself looking for your fingers in the clippings.