To be totally accurate about it, you would pronounce the second day of the week as Mon-day, as Monday is the second day of the week. In relation as to how to pronounce Tuesday, it is pronounced "choose day" most often. If you say it very slowly and deliberately, it can be Tee use day. Accents in a country and the way people pronounce things in different countries also comes into play. In Ireland and Britain, U is commonly pronounced like "you", whereas in the USA and Canada, it is more like oo, as in too. So taking all of these things into consideration, any of the pronunciations are correct. Different people will think of it in different ways. The main thing is that people understand you.