use v5.14;

my $string = 'Lorem ipsum dolor sit amet, consectetur adipisicing elit
+.';
my @skips  = ( 'ipsum', 'sit amet', 'elit' );

my $re = do {
  local $" = '|';
  qr/@skips/;
};

say for $string =~ s/$re//gr =~ m/\b(\w+)\b/g;
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Output:

Lorem
dolor
consectetur
adipisicing
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Update (explanation): The s///r construct returns a new string lacking all "skip" words/phrases. The new string is fed immediately into the second regexp that matches complete words (at least as defined by "\w"). A list is formed, and those are output using 'say' in a loop. If you want to store them instead, change that last line to:

my @keeps = $string =~ s/$re//gr =~ m/\b(\w+)\b/g;
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...or...

my $VAR = [ $string =~ s/$re//gr =~ m/\b(\w+)\b/g ];
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...if you prefer holding a reference to an anonymous array.

Here is one of the way to remove the strings matched in the line from the array.

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

my $line ='Lorem ipsum dolor sit amet, consectetur adipisicing elit';
my @array1 = ('ipsum', 'sit amet', 'elit');

foreach(@array1)
{
 $line =~ s/$_//g;
}
print $line;
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use Modern::Perl;
use Regexp::Assemble;

my $line  = 'Lorem ipsum dolor sit amet, consectetur adipisicing elit.
+';
my @array = ( 'ipsum', 'sit amet', 'elit' );
my $ra    = Regexp::Assemble->new;
$ra->add(@array)->anchor_word(1)->re;

say $ra->as_string; # just for educational purposes
$line =~ s/$ra//g;
say join "\n", split /\W+/, $line;
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G'day neversaint,

Lorem ipsum text is fine as a typesetting tool; however, assuming you've used it here purely as example text, I'm wondering whether it truly reflects your real data. For instance, if your real data contained 'Data::Dumper', is that one or two words and should the '::' be retained; if your real data contained fractional numbers, would the number be considered a complete word and how would you differentiate between the '.' in the number and a '.' terminating a sentence; and so on and so forth.

Anyway, based solely on the example text you've supplied, this does what you want:

$ perl -Mstrict -Mwarnings -E '
    my $line = q{Lorem ipsum dolor sit amet, consectetur adipisicing e
+lit.};
    my @array = (q{ipsum}, q{sit amet}, q{elit});
    my $re = qr{(?:@{[join q{|} => @array]})};
    $line =~ s/$re//g;
    say for split /\W+/ => $line;
'
Lorem
dolor
consectetur
adipisicing
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$ perl -E 'my $line ="Lorem ipsum dolor sit amet, consectetur adipisic
+ing elit."; my @array = ("ipsum", "sit amet", "elit"); my $re=join "|
+",@array;  $r=qr{$re}; say for $line=~/(.*?)$r(.*?)/g'
Lorem 

 dolor 

, consectetur adipisicing
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Note: uses the  s///r substitution regex modifier available with Perl version 5.14+. This is easily worked around if not available.

>perl -wMstrict -MData::Dump -le
"my $line =
   'Lorem ipsum dolor sit amet, consectetur adipisicing elit.'
 ;;
 my @array = ('ipsum', 'sit amet', ' elit ');
 my ($avoid) =
   map qr{ $_ }xms,
   join ' | ',
   map s{ \s+ }' \s+ 'xmsgr,
   map s{ \A \s+ | \s+ \z }''xmsgr,
   @array
   ;
 print $avoid;
 ;;
 my @got = $line =~ m{ (?: $avoid (*SKIP)(*FAIL))?  [[:alpha:]]+ }xmsg
+;
 dd \@got;
"
(?^msx: ipsum | sit \s+ amet | elit )
["Lorem", "dolor", "consectetur", "adipisicing"]
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