You didn't give much to go on but my first hypothesis would be disk I/O. If the file size is small, you could try assigning the entire file to an array and parsing that. Something like

@filetoread = <INFILE>;            # read in file all at once
my $linestooutput = '';            # place to save output until the en
+d
foreach (@filetoread){
    @Line = split /\s+/;  #split defaults to $_
    $linestooutput .= join("\t",@Line[@ColumnNumbers])."\n"; 
}
print OUTFILE $linestooutput;      # write output

# or even shorter
@filetoread = <INFILE>;
$linestooutput .= join("\t",(split /\s+/)[@ColumnNumbers])."\n" foreac
+h (@filetoread); 
print OUTFILE $linestooutput;
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I'm not sure about the speed impact of interpolated splices? I don't imagine that is the issue but you could try something like this

while(<INFILE>)
{
    # get the current line and split into it's columns
    @Line = split /\s+/, $_;

    #print the selected columns to the output
    my $outline .= @Line[$col]."\t" foreach my $col (@ColumnNumbers);
    print OUTFILE $outline,"\n";
}
[download]