(I hope you realize that I really don't care if you have to be mafrish challa from play-dough. Echoing Reb Yirmiah's method, I chose it to illustrate the shittos on Hafrashas Challa in a memorable manner. A less loopy example would be dough that was made to seal pots while they cook, as noted in Shabbas 51b. I assume they threw it out afterwards.)
In other words, is the mitzva of hafrashas Challah a mattir- a utilitarian means of removing an issur and allowing you to eat the remainder, which, therefore, would only need to be done when you want to eat the remainder, or is it inherently requisite when you have dough, a self standing mitzva irrespective of what you intend to do or not do with the rest of it. Or, put it this way: is it dictated only by a desire to generate a specific consequence, or it dictated by current circumstances. For example: The Rambam says that we don't have mitzva to go and shecht an animal. But if one desires to eat meat, the mitzva is to be mattir it by means of Shechita. Rambam 1 Shechita 1:
מצות עשה שישחוט מי שירצה לאכול בשר בהמה חיה ועוף ואחר כך יאכל שנאמר וזבחת מבקרך ומצאנך. The Kesef Mishna saysמצות עשה שישחוט מי שירצה לאכול וכו'. כתב מי שירצה, לומר שאינה מצוה שחייב האדם לעשותה עכ"פ כמו תפילין וציצית שופר סוכה ולולב. In fact, for this reason the Raavad in the Minyan Hamitzvos in the Yad holds that Shechita should not be counted among the mitzvos. Shechita is definitely only a mattir, not an act that is inherently requisite.
Other mitzvos are inherently necessary. For example, you cannot eat a korban until the blood is placed on the Mizbei'ach. What if you cannot eat the korban (e.g., chattas ha'of al hasafeik)? Do you still have to put the blood on the Mizbei'ach? Of course you do! The permission to eat the korban that results from doing the mitzva is not the reason you do the mitzva, it is a tangential result.
So what is the story with Hafrashas Challa? Is it a mitzva in and of itself or only a mattir?
This happens to be a machlokes the Magen Avraham and Reb Akiva Eiger and Rashi (and maybe the Rambam) against the Taz and the Gaon (and maybe the Ramban). The Magen Avraham in OC 8:2 asks why the mishna in Challa allows the bracha on hafrashas challa while seated, when in general brachos should be said while standing. He answers that this mitzva is only a mattir, like Shechita, so it is not like other mitzvos. The Gaon there disagrees, as follows: ודברי מג"א שחלה אינה מצוה, דבריו אין להם שחר, והלא אסור לעשות עיסתו קבין כדי להפקיע חיוב חלה כאמור ביו"ד סי' שכ"ד סי"ד ואמרי' בפ"ג דפסחים [מח,ב,] מאי דעתך לחומרא חומרא דאתי לידי קולא, דמפקע ליה מחלה The Taz in YD 1:17 says clearly that there is a mitzva to be mafrish even if you have no intention of eating the rest and don't need a mattir. Reb Akiva Eiger there mentions the Magen Avraham and holds like him, against the Taz: לא מצאתי זה, דבפשוטו הוא רק כשרוצה לאכלו אסור עד שיפריש תרומה, ובמג"א ריש סי' ח' כתב כן לענין חלה ע"ש, וה"נ בתרומה. Reb Aharon and the Chavatzeles Hasharon (Carlebach, Gilly's brother in law) point out that the passuk in Shlach, Bamidbar 15:19, and a similar passuk by Teruma in Devarim 14:22, use the word "B'achlechem," which seems to support the Magen Avraham. Also, see Rashi in Gittin 47b: ד"ה מדאורייתא: דביכורים מצוה דרמיא עליה היא ולא טבלי לאסור פירות באכילה וכו'. ולא דמי למעשר וכו' דמעשר טביל ואסר ליה באכילה, ולא מצוה דרמיא עליה היא, אלא אם כן אוכלן או מוכרן דקא משתרשי ליה, clearly like the Magen Avraham.
This issue arises in Chalitza as well. Is chalitza only necessary as a mattir or is it a mitzva of its own? What if the Yevama is elderly and there is no chance in the world that she will remarry; is it a mitzva for her to do Chalitza? This is a machlokes between the Chasam Sofer in his Teshuvos EH II 85 (no, because it's only a mattir) and Reb Moshe in his Dibros in Kiddushin He'arah 113 (yes, because it's a mitzva chiyuvis, from the Gemara in Kiddushin 14a.) And what about Shiluach Hakan? Also a machlokes the Chasam Sofer (it's only a mattir) and the Mekubalim (it's a big mitzva.) What about going to the mikva to remove your tum'ah? A machlokes Tana'im, whether Tevilla Bizmana Mitzva (see Yoma 8a and Shabbos 121a).
Interestingly, a closely related issue arises regarding Kiddushin: See Rosh Kesuvos 1:12, who writes:
When I said that the Rambam and the Ramban can be read to agree with, respectively, the Magen Avraham and the Taz, I was referring to their argument in Sefer Hamitzvos Shoresh 12. The Rambam says that he doesn't want to count as mitzvos such actions that are only part of a mitzva, like making the utensils of the Mishkan and making the Mishkan as a whole. The Bahag disagrees. One of the examples of this disagreement is Matnos Kehuna, in which the Rambam combines the separating and the giving into one mitzva. The Ramban argues and says that that's only true in some matanos; the ones that render the mixture tevel prior to separation have two separate mitzvos, the separating and the giving. The ones that do not render the mixture tevel prior to separation have only one mitzva; the separation together with the giving. The Ramban's example is- Challah. He brings from the Sifri that there are two separate mitzvos by Teruma, the hafrasha and the nesina. He also says that if the Rambam were right, it wouldn't make sense to make a bracha on the hafrasha, since that's not the gmar of the mitzva.
The truth is, that the Rambam himself (mitzvos 126) says that the separation of Truma Gedola is a mitzva, and he says the same in his introduction to Trumos in the Yad. It might be said that the Rambam holds that the purpose of the hafrasha is not to permit the remainder, but to generate matanos that you can give to the Cohen. The Ramban clearly holds that it is the generating of the permit on the remainder that is the "purpose" of the mitzva of Hafrasha, because if it were to generate matanos, his distinction between matanos that make the rest tevel and matanos that don't.