What about

use List::Util qw( shuffle );

my @jumpedArray = map { $dataArray[$_*2+0],
                        $dataArray[$_*2+1] }
                  shuffle 
                  0 .. @dataArray/2-1;
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Off topic: Wouldn't it be easier if your data was organized as follows:

my @dataArray = (
   [ \@inputValue1, \@outputValue1 ],
   [ \@inputValue2, \@outputValue2 ],
   ...
);
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That would eliminate any unsightly $_*2+0 and $_*2+1 you have in your code. For example, the shuffling would simplify to the following:

use List::Util qw( shuffle );

my @jumpedArray = map { $dataArray[$_] }
                  shuffle 
                  0 .. $#dataArray;
[download]

 

Update: oops, I was doing a straight copy. Fixed.