Proponents of oil pulling claim that it can remove toxins from our “system” (beyond local effects in the mouth) which must mean that it is removing stuff from the blood through the mucous membranes of the mouth.
Let’s review a few ideas from high school biology to see if this could actually work. No liquid can “pull" a solute across a membrane, the solute must be pushed across the membrane by diffusion. Diffusion is the movement of a substance from a region of high concentration to a region of low concentration. Diffusion stops when the concentrations are equalized.
So a tablespoon of oil can’t absorb any more of the substance than exists in a tablespoon of blood on the other side of the membrane. Absorbing more than that amount would require some source of energy to force the substance into the oil in opposition to the concentration gradient.
The average adult contains 10 pints of blood, each of which contains 32 tablespoons. So adding a tablespoon of oil to the mix essentially increases the body’s fluid volume from 320 tablespoons to 321 tablespoons, or 0.3125 percent. Assuming perfect diffusion of each substance across the membrane, disposal of the oil can therefore remove no more than about a third of a percent of each chemical - toxic or beneficial - from the body. Remember that many vitamins and nutrients are oil-soluble, so oil pulling would remove about 0.3% of those, too.
It seems unlikely that removal of 0.3% of anything from the body is going to have any measurable effect.