Suppressors do make a gun reduce recoil, but they also make the gun much louder.
When a gun is fired, the expanding gas created by the explosion of the cartridge is forced out of the barrel. This gas creates a force that pushes the bullet down the barrel and propels it forward. The suppressor reduces this recoil by trapping some of this gas and redirecting it back down the barrel. This redirected gas creates a counterforce that cancels out much of the recoil.
However, because a suppressor does not eliminate recoil, it still makes the gun much louder than firing without one. Most suppressors increase the decibel level by about 10-15 decibels. So although they do reduce recoil, they also make the gun much louder.