The first half of the Pasuk is teaching us that one may eat Pesulei ha'Mukdashin outside Yerushalayim. What it the second half of the Pasuk coming to teach us?
Yevamos, 73b: It teaches us that a Tahor person is permitted to eat Pesulei ha'Mukdashin together with a Tamei person from the same dish - and we are not concerned that the Tahor person might touch the Tamei one 1 or that he is eating Pesulei ha'Mukdashin that are Tamei. 2
Bechoros, 32b & 33a: See answer #1. And how much more so is a Kohen (the owner of the B'chor under discussion) permitted to invite a Zar and or a Nidah to eat from it. 3 .
What is "Tochlenu ha'Tamei ve'ha'Tahor Yachdav ... " coming to preclude?
Yerushalmi Bikurim, 2:1: It precludes Terumah, which a Tahor Kohen is not permitted to eat together with one who is Tamei, since the latter renders the Terumah Tamei - and a Tahor Kohen is not allowed to eat Tamei Terumah. 1
Yerushalmi (Ibid.): And we learn from here that a Tahor Kohen who eats Tamei Terumah transgresses an Asei. See also Torah Temimah, note 90.
Why does the Torah compare a B'chor Ba'al-Mum to a deer and a gazelle?