Assalamu Alaikum W w Is it permissible to eat small food pieces which are between two teeth space inside mouth, Because some time I use to pick out beef pieces from teeth space by using thooth picker and eat that particles

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

It is permissible for one to eat the food remnants between his teeth if he brings them out by his tongue and the like, but he should not eat what he has taken out by a toothpick and the like. This distinction is mentioned in a Hadeeth narrated by Abu Hurayrah that the Prophet said: "…If one eats, then whatever he takes out (from between his teeth) by using a tooth stick, he is to spit it out, and whatever he can take out by dislodging it with his tongue, he may swallow it (eat it); whoever does that has done well, and whoever does not,  there is no harm in it...” [Ahmad and Abu Daawood]

What is stated in regard to the wisdom of this distinction is what the author of the book Mirqaat Al-Mafaateeh said: “Al-Muth-hir said that the Prophet ordered that whatever one can take out by his tongue from between his teeth, he may swallow it (eat it); contrarily to what a person takes out by using a tooth stick because some blood may come out by using a stick and the like [and it is known that it is forbidden to swallow blood].”  

A similar explanation was given by Al-‘Atheem Abaadi the author of 'Awn Al-Ma'bood in his commentary on Sunan Abu Daawood.

Allaah Knows best.