Firstly, note, getting each slice only operates on the outer tuple and that the lists inside are not sliced at all.
The first part of the expression [0:] means everything after and including the first element which means everything. This, therefore, does nothing. The next section [1:] means everything after and including the second element which means everything except the first element so ["one", "two", "three"] is thrown away.
tuplun = (["one", "two", "three"], ["hello", "scope"], ["pedro"])
tuplun2 = (tuplun[0][1:],)+tuplun[1:] # The comma is there to declare it is a tuple