There were at least two effects of the Stamp Act on American liberty. One effect was on the American liberty to govern themselves while the other was on their liberty to be tried by a jury of their peers.
The Stamp Act, of course, was passed by a Parliament that did not have American representatives. Colonial assemblies were not consulted. This took away from the liberty that Americans felt they had to govern themselves.
Secondly, the Stamp Act took jurisdiction over cases arising under it and gave that jurisdiction to vice-admiralty courts. Cases in these courts were heard by judges only, without juries. This took away the liberty of trial by jury and set up a system where rights and liberties were at the mercy of the government only.