$Type contains the splitted result of field->mime_type. You are however splitting at the character '/' therefore it is impossible that $Type contains the pattern 'multipart/mixed'. If $field->mimetype returns 'multipart/mixed' then $Type will contain 'multipart' and $subtype will contain 'mixed'.
Update:

looking at the code i was also confused by the way you created your fields 'object'. You just assign the string 'Content-Type' to a variable called $field and rely on perl symbol table voodoo to dereference it to MIME::Field::ContType. I recommend that you have a look at the syntax used in the example of MIME::Field::ContType. It might help you getting closer to a solution.

Another problem is: assuming the desired information is contained in the $header - you aren't accessing it anywhere.

If you want to have a look at some working examples you might try searching google for o'reillys perl cookbook. It contains complete example scripts which might help you solve common problems.