Think it through, your cypriot company has lots of money in the account after some successful trading which is legally not your money, it's the company's. So you decide to pay some of it to yourself as either a salary or a dividend perhaps.
The country you are resident in has taxes on both of these income streams and so you would write on your tax return at the end of the year what you earned and pay the tax accordingly like any other resident of the countrywhere you live. 30% 40% whatever it is, PLUS you'd have already paid 10% in Cyprus!
The alternative is to write a big Zero on the tax return and say that you have had no income. This only works to a point before they investigate your lifestyle, expenses etc and realise that you are living in their country, with a posh car and 3 kids and your income cannot possibly be zero. Then you get done for not declaring overseas earnings and fined. :-0
The only thing the company does is allow you to delay paying yourself the money until you want it. For example, UK dividend taxes are quite low up to a certain amount per year, so you could drip feed the money out of the company over several years as dividends without going into the next tax bracket. :idea:
However, if you're good at what you do, you'll find the money stock piles in the company's account because you are not paying it to yoursef as quick as you're earning it and you can't spend it without paying masses of tax!
Hope that helps