In theory, an increase in taxes leads to a decrease in gross domestic product while a decrease in taxes leads to an increase in GDP. Of course, there are many variables that exist in the real world that make this relationship much less clear than it is in theory.
According to many economists (generally those who believe in supply-side economics), an increase in income taxes causes a decrease in the supply of labor. People essentially get paid less to work and are therefore less willing to work. A lower supply of labor leads to lower GDP.
There is also a demand-side argument to be made. In that way of looking at things, an increase in income taxes reduces the amount of money that people have to spend. This makes aggregate demand go down, causing GDP to do down as well.
Thus, most economists believe that, whatever the mechanism, increased taxes cause GDP to be lower than what it would be if taxes were not increased.