Your difficulty may have been from not declaring variables with my. When you use strict; you have to be strict. In any case, substr would be effective for this. Assuming it's sane to have the DNA file all in memory:

#!/usr/local/bin/perl -w
use strict;

open SEQ, "< dna.file" or die $!;
my @dna = <SEQ>;
close SEQ or die $!;

chomp @dna;
my $dna = join '', @dna;
@dna = map {length} @dna;

open LOCS, "< positions.input" or die $!;
for (<LOCS>) {
    # I don't know how your data is counted, watch for fencepost error
+s
    my ($start, $end) = split " ";
    substr( $dna, $start, $end - $start) =~ tr/CGAT/X/;
}
close LOCS or die $!;

{
    local $\ = $/;
    open OUTFILE, "> $$.output" or die $!;
#    print OUTFILE for map { substr $dna, 0, $_, '' } @dna;
    print OUTFILE substr( $dna, 0, $_, '') for @dna;
    close OUTFILE or die $!;
}
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There are several tidbits here for a student of perl. Untested but It Ought To Work(TM). It might be worthwhile to make this do without hardcoded file names.

Update: I like map too much. Modified output loop to save memory.

After Compline,
Zaxo