Its complicated.
Yes, cells need sugar to respire and metabolize, however, cells can obtain this energy from other metabolic means. Ketogenesis is one example of energy production with reduced sugar intake. However, this type of diet I wouldn't suggest because too high of fat and too high of protein could lead to steatoheptatic disorders, possibly pancreatitis and fatty liver disease because it might put your pancreas and liver into overdrive to compensate. The key thing here to remember is, glycolysis fermentation has been theorized by Otto Warburg and others as one of the main ways in which cancers feed. In other words, when sugars are fermented and produce lactic acid, it creates carcinogenic environments and is a warning sign of carcinogenic metabolism. Now normally, glucose in standard metabolism gets oxidized (yet another paradox about metabolism is the role of oxygen which I'll explain below) and turned into pyruvate through the citric acid cycle and if the electron transport chain is working normally then fermentation does not occur. So a lot of cancers may be caused by some sort of dysfunction with how the cell metabolizes. However this isn't to say stop eating sugars altogether (such as fruits and vegetables) your body still needs fruits and vegetables for important cancer preventative phytochemicals, this is why so many cancer diet protocols are so demanding of a higher intake of fruits and vegetables. Anyway the troubles with oxygen is that we need it to live, but it is also killing us. So while we give our bodies antioxidants to reduce the amount of superoxides and hydroxyl groups which may contain free radicals that can damage our DNA/RNA, we still need the proper balance of oxygen to keep from producing an anaerobic environment for which cancer cells seem to thrive in. It is a gigantic act of balance and this is called "homeostatic balance" - when we are too far one way or the other it can cause problems. Also cancer feeds in more than one way, recent research shows certain RAS cancers feed off of high amounts of serum proteins through a process called macropinocytosis and can starve the body of protein thus leading to hypoalbuminemia.
Anyway long story short, yes your body needs sugar to live, but do you need processed sugar to live? No. Can you survive without buying the bleached sugar? Yes. Can you survive without refined sugar (e.g. pastries, cakes, candies, sugar in your tea, sugar in your coffee, sugar in your bread, ADDED sugars no present already naturally?) Yes, absolutely, you can survive without processed or refined sugars added to your foods, and should avoid refined sugars as much as you possibly can. NATURAL sugars however, the NATURAL sugars present in fruits and vegetables are fine for you, because again, your brain only knows how to metabolize glucose (as far as I know... whereas the rest of your body is better at ketogenic metabolism). I wouldn't go so far as to suggest full blown ketogenesis diet but I would suggest reduced refined ADDED sugars in our diets, greatly reducing the amount of sugar we use every day could help keep us healthier, help prevent cancer and diabetes.