Clean means to remove the dirt from something. When we use the word wash, it means with water. So, we usually use clean with acts like wiping tables, surfaces, etc. with a cloth, and wash for things like dishes, the outside of a car, etc.
As for wipe, it's the action of using a cloth, tissue, or even hand to remove dirt from something. For example, 'He wiped his forehead with his hand.' or, 'She wiped the table with a cloth.'
Clear just means to move unwanted items from a place. For example, 'Can you clear the table so that we can have dinner?' or I cleared the room from all the mess.'