For comparison, this uses HTML::TreeBuilder.

You have nine groups of seven rows so we process seven rows at a time loading the data into an AoH. I think it reads fairly well and maintaining it ought to be relatively straight forward if your HTML changes.

#! /usr/bin/perl

use strict;
use warnings;

use Data::Dumper;
use HTML::TreeBuilder;

my $file_name = q{la.html};
my $t = HTML::TreeBuilder->new_from_file($file_name)
  or die qq{cant build tree from *$file_name*: $!};

my @trs = $t->look_down(_tag => q{tr});

my @db;
while (@trs){
  my @fields = splice(@trs, 0, 7);
  
  my %rec;
  $rec{group} = $fields[0]->as_text;
  $rec{type}  = $fields[1]->as_text;
  
  my @tds;
  @tds = $fields[2]->look_down(_tag => q{td});
  $rec{level} = $tds[1]->as_text;

  for my $field (3..5){
    @tds = $fields[$field]->look_down(_tag => q{td});
    $rec{$tds[0]->as_text}  = $tds[1]->as_text;
    $rec{$tds[2]->as_text}  = $tds[3]->as_text;
  }

  $rec{note} = $fields[6]->as_text;
  
  push @db, \%rec;
  
}
print Dumper \@db;
[download]

extract and the note field shortened for brevity:

$VAR1 = [
          {
            'Saving Throw:' => 'None',
            'Casting Time:' => '1',
            'Area of Effect:' => ' 10 ft.×10 ft./level path',
            'Range:' => 'Touch',
            'Duration:' => '3 rds. + 2 rds./level',
            'note' => ' By means of this spell... or mica.',
            'Components:' => 'V, S, M',
            'group' => 'Detect Illusion',
            'level' => '1',
            'type' => '(Divination)(Mentalism)'
          },
          {
            'Saving Throw:' => 'Special',
            'Casting Time:' => 'Special',
            'Area of Effect:' => 'Script reader',
            'Range:' => 'Touch',
            'Duration:' => '1 day/level',
            'note' => ' This spell enables the ....',
            'Components:' => 'V, S, M',
            'group' => 'Illusionary Script',
            'level' => '3',
            'type' => '(Illusion/Phantasm)'
          },
# ... <snipped>
        ];
[download]

Oh, and btw, 38 lines. :-)