Opening foreign letter with edge of thumb makes bad mark (6)
'bad mark' is the definition.
(stigma is the mark or taint of something bad)
'opening foreign letter with edge of thumb' is the wordplay.
'opening' means one lot of letters goes inside another (some letters open a gap in others).
'foreign letter' becomes 'sigma' (Greek letter).
'with edge of thumb' becomes 't' (I can't explain this - if you can you should believe this answer much more).
'sigma' enclosing 't' is 'STIGMA'.
'makes' acts as a link.
(Other definitions for stigma that I've seen before include "Mark of shame, stain on reputation", "Mark of dishonour", "Blot", "Brand or mark of infamy", "Badge of shame".)