How to put a variable in an array?

You want:

 my ( @array1, @array2 );    
 while (...) {
     my ($start, $end) = ...;
     push @array1, $start;
     push @array2, $end;
 }

 my @sorted_indexes = sort {
    $array1[$a] <=> $array1[$b]
       ||
    $array2[$a] <=> $array2[$b]
 } 0..$#array1;
 @array1 = @array1[@sorted_indexes];
 @array2 = @array2[@sorted_indexes];

With a proper CSV parser:

 use Text::CSV_XS qw( );

 my ( @array1, @array2 );    
 my $csv = Text::CSV_XS->new({ binary => 1, auto_diag => 1 });
 while (my $row = $csv->getline($fh)) {
     my ($start, $end) = $row->[2] =~ /(\d+) \/ (\d+)/
        or die("Bad data");

     push @array1, $start;
     push @array2, $end;
 }

By the way, many avoid parallel arrays and would prefer

 my @array;    
 while (...) {
     my ($start, $end) = ...;
     push @array, [ $start, $end ];
 }

 @array = sort { $a->[0] <=> $b->[0] || $a->[1] <=> $b->[1] } @array;

Probably you are looking for this:

my ($start, undef, $end) = m{"((\d|\s)+) / (\d+)"};

It is more specific on the "-s, so it finds the third item in your csv line.
It also uses { and } for quoting, because | is used for specifying alternatives in the pattern.
There are three submatches in the pattern (three pairs of (), two nested), but we use the second (the nested one) only to apply the quantifier + to the alternatives (digits or spaces), so we discard that submatch result with assigning it to undef on the left.

You can collect the pair as a record in an array of references, and still sort the array using a field in the record. It's tricky looking syntactically, but easily done. Basically a push @ary, [ $2, $3 ];

Then to sort the records by a particular field you could do this:

use strict;
use warnings;

$/ = "\n";

my $line;
my @records = ();

while ( $line = <DATA> ) {
  if ($line =~ m|(.* )(\d+) / (\d+)|) {
    push @records, [$2, $3];
  }
}

sub getSortedRecords {
  my ( $field, $direction ) = @_;
  return sort {
      my($r1, $r2) = ($a, $b);
      ($r1, $r2) = ($b, $a) if $direction cmp 'descending';
      $$r1[ $field ] <=> $$r2[ $field ];
  } @records;
}

print "Ascending, fld 0\n";
for ( getSortedRecords( 0, 'ascending' ) ) {
  print $$_[0], " / ", $$_[1], "\n";
}

print "\nAscending, fld 1\n";
for ( getSortedRecords( 1, 'ascending' ) ) {
  print $$_[0], " / ", $$_[1], "\n";
}

print "\nDescending, fld 0\n";
for ( getSortedRecords( 0, 'descending' ) ) {
  print $$_[0], " / ", $$_[1], "\n";
}

print "\nDescending, fld 1\n";
for ( getSortedRecords( 1, 'descending' ) ) {
  print $$_[0], " / ", $$_[1], "\n";
}


__DATA__
"ATSMM","CCC","43 676 1 / 4"
"AERCM","XXX","54 320071 2 / 3"
"ATSMM","CCC","43 676 3 / 2"
"AERCM","XXX","54 320071 4 / 1"

Out >>

Ascending, fld 0
4 / 1
3 / 2
2 / 3
1 / 4

Ascending, fld 1
1 / 4
2 / 3
3 / 2
4 / 1

Descending, fld 0
1 / 4
2 / 3
3 / 2
4 / 1

Descending, fld 1
4 / 1
3 / 2
2 / 3
1 / 4