yes, you have got to switch it off. Take the food out, wrap it quickly, put it in the largest cardboard boxes you can find, and wrap them. Big sheets of plastic or paper will be fine, wrap loosely so there are are layers of air. The food will stay frozen for some hours. If it thaws, cook and eat the expensive stuff first, and ice-cream which can't be refrozen. You can safely re-freeze cooked food so you can make casseroles.
the freezer will obviously be lighter once empty. Taking the food out will also let it defrost faster.
If it is difficult to move, consider an "appliance trolley" which is a frame with wheels. The appliance is less likely to fall off than if you use appliance rollers. You can adjust the frame so the apliance feet are on it.
Biosch and Siemens freezers often have wheels at the back, so if you tilt them back enough to get the front feet off the floor, they can be wheeled around. Other brands may also do that.
If it is a frost-free freezer, it will have a fan and air ducts hidden inside the back. If these are choked with ice, it is essential to let it defrost long enough for it all to drip out. It may take more than a day. Wait until there are no more drips and, when wiped, it stays dry.
If you pull a fridge or freezer away from the wall, you can vac the dust and fluff off the evaporator coils, which will make it more efficient. Observe the dish on top of the motor where water goes. Clean it out and make sure no water spills onto electrical parts.
If you check the instruction book, you might find there is a defrost setting that will turn it off without you having to pull the plug out