You were very close to solving the problem. You just need to repeat the search multiple times, as perl will continue the search when the last one ended.

use strict;
use warnings;
use Data::Dumper;

my $data;

# Modifying $/ in a limited context to avoid 
# affecting other areas of the code.
{
  local $/;
  $data = <DATA>;
}


#
# Create the regular expression using qr{}x as it makes
# the pattern much easier to follow (and maintain)
#
my $pattern = qr{
  (\d+-)
  (\d+-)
  (\d+)
  (\s*/\s*)
  (\d+)
  (\s*/\s*)
  (\d+)
}x;

my @list;
while ($data =~ /$pattern/g) {
  push @list,[$1,$2,$3,$4,$5,$6,$7];
}
print Dumper \@list;

__DATA__
      PART NAME         QUANTITY    SECTION/FIGURE/ITEM

      Widget1               1       72-33-00/ 23/ 85
      Widget1               1       75-20-00/ 11/ 10
      Widget2               1       72-33-00/20/10
      Widget2               1       72-33-00/20/70
      Widget2               1       72-00-33/2/1
      Widget2               1       72-00-33/2/20
      Widget2               1       73-12-00/4/1
      Widget2               1       73-12-00/4/220
      Widget2               1       73-12-00/3/10
      Widget2               2       79-20-00/9/1
      Widget2               1       79-20-00/5/1
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Note that I defined the regex before the loop. This makes the logic easier to follow, particularly when you use the 'x' modifier.