Some other monk will probably post a one-liner, but this should work, and hopefully it's easy to understand. If you don't know of them already, have a look at chr and quotemeta, and maybe ord for good measure.

my @ascii_be_gone = (215,220,224,226,231,232,233,234,235);
my @chars_to_go   = map { chr } @ascii_be_gone;
my $pattern = join '|', map { quotemeta } @chars_to_go;
$str =~ s{$pattern}{}g;
[download]

Since they're characters, not strings, you can use a character class instead of an alternation.

my @ascii_be_gone = (215,220,224,226,231,232,233,234,235);
my @chars_to_go   = map { chr } @ascii_be_gone;
my ($pattern) = map { qr/[$_]/ } join '', map { quotemeta } @chars_to_
+go;
$str =~ s{$pattern}{}g;
[download]

You could use tr[\xd7\xdc\xe0\xe2\xe7-\xeb][]d;

The \xdd escapes (for hex, or \0dd for octal digits, etc.) documented in perlop (search for "Quote and Quote-like Operators") work within a tr statement.