Does a mirena break or stretch a hymen?

Yes: To insert an IUD such as Mirena, a speculum is inserted in the vagina so the cervix can be visualized, and this stretches the hymen. Women who have used tampons have usually stretched the hymen and do not find the speculum to be painful when inserted.

Merina IUD: to insert merina the health professional need to insert a speculum to be able to visualise the cervix and insert the devise, so there has to be some stretch on the hymen. but weather this break it or no depends on the type of hymen, best to consult the gynaecologist who inserted the merina

Hymen: When a mirena is inserted it will perforate the hymen. Can't be introduced with out damaging it

Yes but: While the hymen may be stretched during insertion things are variable and the so-called "intact" hymen is not ubiquitous. You may therefore have no troubles at all with the insertion. Generally if you've previously been sexually active or engaged in sexual activity this shouldn't be an issue although if not anaesthetised the insertion into the uterus itself can be sore initially