In general, the Halacha prohibits discarding the P’solet (waste) from the food, and only permits the reverse-selecting the Ochel (food) from the P’solet. Nevertheless, the Be’ur Halacha brings down a Machloket (disagreement) between the Poskim whether discarding the undesired element “Derech Achilah”-during the act of eating is permitted. Mahari Abulafia permits it, and Mahari Tas (R’ Yom Tob Sahalon, 1559-1638, Tsfat) prohibits it. This question is actually a Machloket Rishonim (earlier authorities), with the Ramban holding that it is permitted and the Rosh holding that it is prohibited. Hacham Ovadia rules that it is prohibited. However, there can be room to be lenient in conjunction with other factors.
It is always prohibited to remove the waste from a mixture, even while eating.