I have seen that when one of our community elder died and when they put on tallit they cut out the tzitzit part and let him put only the garment. Why is this done to a dead person? Is there a source for this and a good reason ?
The source is from Shulchan Aruch Yoreh Deah 351:2
אֵין קוֹבְרִין אֶת הַמֵּת אֶלָּא בְּטַלִּית שֶׁיֵּשׁ בּוֹ צִיצִית. הַגָּה: וְיֵשׁ אוֹמְרִים דְּאֵין צָרִיךְ צִיצִית (טוּר בְּשֵׁם י''א). וְנָהֲגוּ לְקָבְרוֹ בְּצִיצִית, אַךְ שֶׁפּוֹסְלִין תְּחִלָּה הַצִּיצִית, אוֹ כּוֹרְכִין אֶחָד מִן הַכַּנְפוֹת.
The Shulchan Aruch writes that one buries a dead in a talit with tzitzit. The Tur writes that some say one doesn't need tzitzit and the Rema rules that one uses a talit but first invalidates one of the tzitzit.
JVL comments this is indicating the deceased is no longer required to perform rituals.
The Ramban (Milchamot Moed Katan 16a s.v. amar) argues that they should put tzitzit on the tallit that the deceased is buried in so that the deceased isn't embarrassed that he isn't wearing tzitzit when the resurrection of the dead takes places in the Messianic era. This opinion is codified by the Mechaber in Shulchan Aruch YD 351:2.
The Aruch HaShulchan (ad. loc.) brings that big sages like the Vilna Gaon instructed to be buried with kosher tzitzit but were prevented to do so by some spurious occurrences during the burial. This was taken by some to be a sign from heaven that the Rama should be followed and the tzitzis need to be invalidated right before the burial into the ground.