How can I remove characters that are not supported by MySQL's utf8 character set?

MySQL's utf8mb4 encoding is what the world calls UTF-8.

MySQL's utf8 encoding is a subset of UTF-8 that only supports characters in the BMP (meaning characters U+0000 to U+FFFF inclusive).

Reference

So, the following will match the unsupported characters in question:

 /[^\N{U+0000}-\N{U+FFFF}]/

You could use it as follows:

• Remove unsupported characters:

  s/[^\N{U+0000}-\N{U+FFFF}]//g;
  

• Replace unsupported characters with U+FFFD:

  s/[^\N{U+0000}-\N{U+FFFF}]/\N{REPLACEMENT CHARACTER}/g;
  

• Replace unsupported characters using a translation map:

  my %translations = (
     "\N{MATHEMATICAL ITALIC SMALL EPSILON}" => "\N{GREEK SMALL LETTER EPSILON}",
     # ...
  );
  
  s{([^\N{U+0000}-\N{U+FFFF}])}{ $translations{$1} // "\N{REPLACEMENT CHARACTER}" }eg;
  

For example,

use utf8;                              # Source code is encoded using UTF-8
use open ':std', ':encoding(UTF-8)';   # Terminal and files use UTF-8.

use strict;
use warnings;
use 5.010;               # say, //
use charnames ':full';   # Not needed in 5.16+

my %translations = (
   "\N{MATHEMATICAL ITALIC SMALL EPSILON}" => "\N{GREEK SMALL LETTER EPSILON}",
   # ...
);

$_ = "𝜀C = -2.4‰ ± 0.3‰; 𝜀H = -57‰";
say;

s{([^\N{U+0000}-\N{U+FFFF}])}{ $translations{$1} // "\N{REPLACEMENT CHARACTER}" }eg;
say;

Output:

𝜀C = -2.4‰ ± 0.3‰; 𝜀H = -57‰
εC = -2.4‰ ± 0.3‰; εH = -57‰