If, as suggested by your sample code & data, your array elements contain no spaces, then a very simple, and relatively efficient mechanism would be:

@bigarray = qw(this is the main array from which to delete elements);;
@smallarray = qw(delete elements);;

($temp = "@bigarray") =~ s[@smallarray][] and  @bigarray = split ' ', 
+$temp;;

print for @bigarray;;
this
is
the
main
array
from
which
to
[download]

If your elements can contain spaces, then the same technique could be utilised, by using a different separator char -- eg. $;. It is only slightly more complex;

@bigarray = qw(this is the main array from which to delete elements);;
@smallarray = qw(delete elements);;

$b = join $;, @bigarray;;
$s = join $;, @smallarray;;

$b =~ s[$s][] and @bigarray = split $;, $b;;

print for @bigarray;;
this
is
the
main
array
from
which
to
[download]