The first Mishnah in Terumot discusses those individuals that are not able to separate terumah. The second Mishnah qualifies one of those on that list and explains that the law is different for a cheresh (deaf person) that can speak. The Mishnah teaches the even though they should ideally not separate terumah, if they do, it is effective. Unlike a regular cheresh, this individual is considered as have da'at (understanding of halachic significance). Consequently his separation of terumah would work. We shall however try to understand why he should ideally not separate terumah.
The Bartenura explains that this is because ideally one should hear the beracha that they recite. Since a beracha is recited prior to separation, and he would not be able to hear his beracha, ideally he should not separate terumah. Nevertheless, since the separation of terumah is not dependant on the beracha, if the cheresh did separate terumah it would work.
The R' Chaim (Derech Emunah 4:38) explains that normally a cheresh would indeed recite his own berachot and recite them out loud. Nevertheless, in this case since it is possible for him to designate a shalich to separate his terumah, he should do so. It follows that if there is a case of sefek tevel where a beracha would not be recited, there would be no problem for this cheresh to separate his own terumah.
In the Biur Halacha, R' Chaim cites the Maharil who understands our Mishnah differently. The cheresh can surely perform hafrasha for himself since his situation is bedieved (not ideal). The Mishnah instead is referring to whether one can nominate a cheresh as a shaliach.
R' Chaim however continues that the other rishonim disagree. He cites the Rashbatz who assumes the Mishnah is referring to the cheresh separating his own terumah. He asks, based on the Mishnah, how then can a cheresh recite birkat hamazon or recite megillah? He explains the cheresh would have no issue regarding those mitzvot since his situation is bedieved. It is only regarding terumah where he has the option to use a shaliach that we direct the cheresh to do so. The Rashbatz notes that the fact that the Rambam's only mention of a speaking cheresh is in the laws of Terumot as a proof that it is the exception.
Interestingly R' Chaim also cites the Meiri who writes that while this cheresh can perform mitzvot for himself, he cannot, ideally, motzi others in the performance of a mitzvah. The Meira includes birkat hamazon, megillah and the beracha of terumah as examples. What is the case of "birkat terumah" for which the cheresh cannot perform for others? At first it would seem to be the case of the Maharil that the cheresh cannot act as a shaliach for another. Alternatively, it might be where he recites the beracha for other that are going to do hafrasha. R'Chaim however feels that those suggestions are forced. Instead, R' Chaim suggests that since the act of hafrasha terumah also permits the food to others, that act is considered as being "motzi" others. Consequently, much like the Rashbatz, the cheresh should ideally select use a shaliach to perform the hafrasha. R' Chaim notes that the law would be different for mezuzah or ma'akeh (affixing a railing) where it is an obligation placed on the individual, the cheresh would be able to perform the mitzvah himself. Hafrashat terumah is different in that there is no personal obligation to find tevel to perform hafrasha.
Note however that there is a difference between R' Chaim's understandings of the Rashbatz and the Meiri. According to the Rashbatz the issue is that ideally one should hear the beracha they recite. The cheresh's situation is one that is bedieved and therefore he can recite his own berachot, unless he has another option, like in the case of terumah. According to the Meiri however, the issues is the cheresh's inability to motzi others. Since hafrashat terumat permits the food to everyone, it is a mitzvah that impacts others and therefore someone else should perform that mitzvah. That being the case, perhaps the Meira would maintain, the even in a case of safek tevel, where a beracha is not recited, the cheresh should still use a shaliach.
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