The ATARN link above describes the action of shooting very well. Flip shooting is older than you probably thought
The bow has to be smaller than an arrow shooting bow because the projectile weight is generally much lighter. A larger more powerful bow would be damaged by shooting something so light, the weight of the bow limbs would retain the majority of the kinetic energy at the end of the power stroke and so wreck themselves with powerful vibrations after the bowstring snaps taught.
You could scale it up to shoot bigger ammo, but then bigger targets are more valuable and worth risking an arrow for. The pellet bow is used on small targets where missing and losing an arrow would be unacceptable. A sling delivers much bigger ammo to huge distances, but with rather less accuracy. Good for herding sheep and bombarding armies, less good for hunting.
Some photos of pellet bows in Vietnam, and also the claim that they invented the fork-n-rubber slingshot which was then brought to Europe by the colonial French (doubtful!) : http://www.binhdinh-salongcuong.org/GB_DISCUSSION_%20Medieval%20Weapons_Eighteen%20Sections.html
A Thai pellet bow. This has a carved wooden guard bound in front of the pouch to protect against bow hits. I have seen the same on pellet bows from India. http://web.prm.ox.ac.uk/weapons/index.php/tour-by-region/oceania/asia/arms-and-armour-asia-87
[The direct link doesnt work, so type 'pellet bow' into the search box on the page it takes you to.]
Here is one that shoots TTB 'Through The Bows', there are other pellet bows with hand guards too: http://paleoplanet69529.yuku.com/reply/446434/Re-Interesting-double-pellet-bow