There are two basic reasons why one should not speak external matters during a beracha: the disgrace to the beracha as well as the mixing of words, which renders the beracha nonsensical.
The central responses of Kedusha (“Kadosh…”, “Baruch k’vod…”[2]) and Kaddish (“amen yehei shmeih rabba” and amen to “…da’amiran b’alma”[3]) are so important that one must stop and recite them even when he is in the middle of reciting Kri’at Shema or its berachot.[4] This is based on the mishna’s statement[5] that one may respond at these times to greetings extended by a distinguished person. Most Rishonim posit that responding to these public praises of HaShem is no less appropriate at that time than responding to a human being. If this is true during Kri’at Shema and almost any time other than during Shemoneh Esrei,[6] then it is certainly not a disgrace to interrupt Asher Yatzar for such responses.
A complication arises, however, because answering can make the beracha one is reciting nonsensical. The Kesef Mishneh[7] writes that one does not answer “amen yehei shmeih rabba” during birchot hanehenin (on food) and birchot hamitzva. However, he does not specify why these berachot differ from others.
Some Acharonim[8] posit that the distinction is between the short berachot of the Kesef Mishneh’s examples and the long berachot of Kri’at Shema.[9] Short berachot are not more important than long ones, but they are more likely to be ruined by extraneous statements. As the Ben Ish Chai[10] comments, a statement of “Baruch ata … melech ha’olam kadosh kadosh …” makes no sense. In addition, in the case of a short beracha, one is not simply interrupting one topic, switching to another, and then returning to the first; he is also detaching the opening of the beracha from the statement to which it is supposed to connect. This is particularly problematic, because one has already said HaShem’s Name in beracha form. It is then forbidden to interrupt the recitation of the beracha even for the sake of answering Kedusha or Kaddish.
While there are no good places to stop in a short beracha, in a long beracha, there are some better and some worse places to break. The Mishna Berura[11] discusses the second half of Baruch She’amar (from “Baruch ata…”), which is a long beracha with a short “beracha ending” (“Baruch ata HaShem melech mehulal batishbachot”). He rules that one may not answer Kaddish and Kedusha after saying the final “HaShem” until he has completed “batishbachot.” Ishei Yisrael[12] applies this logic to the beginning of long berachot in general, forbidding one to answer devarim shebekedusha from the beginning of the first “baruch ata HaShem” until he has added on to the basic “template” a few words that create a coherent idea that gives the beracha some significance.
Applying these concepts to your example of Asher Yatzar (which is a long beracha), it seems that after saying “Baruch … asher yatzar et ha’adam b’chochma,” the beracha is significant,[13] and one can then answer Kaddish and Kedusha until reaching HaShem’s Name at the beracha’s end.
We must further consider the case of one who is in the middle of reciting a long beracha and has said enough of it such that the opening is significant, and he now wishes to answer Kaddish or Kedusha in the middle of a phrase. The Shulchan Aruch[14] rules that one should stop for Kaddish and Kedusha even in the middle of a pasuk of Kri’at Shema. There is a machloket regarding whether one may do so only at a logical pausing point in the pasuk.[15] Whereas the Mishna Berura urges planning in advance to avoid this situation, he does allow stopping anywhere, if necessary, but he writes that after answering, one must return to the beginning of the pasuk. Applying this to the case of a long beracha, we would conclude that it is similarly proper to be at a good place mid-beracha to pause to answer, but if necessary, one can answer in the middle of a long beracha and then return to a place that makes the continuation coherent.[16]
Finishing the beracha quickly before answering is generally preferable. However, that is the case only if your kavana will not be significantly diminished as a result.