If I have understood correctly, you could do a split using look-around assertions, see perlre, either using a look-ahead to split before your enzyme or a look-behind to split after it.

use strict;
use warnings;

open my $seqFH, q{<}, \ <<'EOD' or die qq{open: << HEREDOC: $!\n};
CAGTTTCGATCGAATC
ATTATTGGATCCGCAT
GCGTCAGGATCCAATC
EOD

my $sequence = join q{}, map { chomp; $_ } <$seqFH>;
close $seqFH or die qq{close: << HEREDOC: $!\n};

print qq{Sequence:\n     $sequence\n};

my $enzymeSeq     = q{GGATCC};
my $rxSplitBefore = qr{(?=$enzymeSeq)};
my $rxSplitAfter  = qr{(?<=$enzymeSeq)};

print qq{Splitting before $enzymeSeq\n};
my @chunksBefore  = split m{$rxSplitBefore}, $sequence;
print qq{     $_\n} for @chunksBefore;

print qq{Splitting after $enzymeSeq\n};
my @chunksAfter   = split m{$rxSplitAfter}, $sequence;
print qq{     $_\n} for @chunksAfter;
[download]

The output.

Sequence:
     CAGTTTCGATCGAATCATTATTGGATCCGCATGCGTCAGGATCCAATC
Splitting before GGATCC
     CAGTTTCGATCGAATCATTATT
     GGATCCGCATGCGTCA
     GGATCCAATC
Splitting after GGATCC
     CAGTTTCGATCGAATCATTATTGGATCC
     GCATGCGTCAGGATCC
     AATC
[download]

I hope I have guessed correctly and this is of some use.

Cheers,

JohnGG

Update: Corrected die text.