Where to start on this one? In no particular order:
1. The TDA does not have a "betting line" or "forward motion" rule. The default standard for automatically binding a bet is chips released and hitting the table surface (Rule 42). This does not mean, however, that a TD can't rule a bet binding with something less than full chips released (see note 4 below).
2. That said, the TDA recognizes that some TDA-member venues still have and use betting lines (some still have them marked on the table but don't use them)... and if there are betting lines / forward motion rules, house standards apply. (Rule 14-B).
3. SO, start with a chips released standard..... the player pushes out a large stack of chips, then begins cutting out a smaller stack. Well, that usually involves both hands. Clearly, once the hands leave control of the large stack, it is ALL in jeopardy of being declared bet... it is pushed forward, on the table surface, and the player is cutting out chips from it.
4. EVEN IF a player technically retained such control that you could say the chips weren't "released" until the smaller stack is cut out, the TD still has wide latitude to rule it a bet of the entire stack if he or she thinks it is "in the best interest of the game" (Rule 1), and or if he or she thinks the full bet is the player's intention (Rule 3 and elsewhere)... and if it wasn't the player's intention, that's the player's fault, not the TD.
5. EVEN IF a TD rules that the player can cut out the chips in a specific circumstance, your question asks if this is "okay". Ruling it an acceptable bet in one instance does not make it "okay". The player may still be subject to penalty for using such disruptive betting gestures. And clearly, nobody wants to see this be a routine means of betting, so it's never okay.
There's a really great video you can refer to from the WSOP a few years ago where a player moved a stack forward then pulled it back. Jack Effel ruled it a non-bet because the chips weren't ever released from player control. However when a player asked him if it was "okiay" to bet like that he replied "no it's not okay"... leaving open the door for penalty for such a move.
ALSO, keep in mind on your first scenario you say the house has a betting line in effect, so the bottom line really is that house standards apply because the TDA uses chips-released.
To your second scenario, there is no betting line. So here the above comments 1-5 apply... What we know for sure is that this type betting is not acceptable and must be given a warning or stronger penalty. Whether you rule it a binding bet of the entire stack or not depends on the exact circumstances, but the visual I get is such that I normally would rule it a binding bet of the entire amount. I'm not fond of the idea that the guy can keep a tight control over the larger stack while manipulating out a smaller stack from it. Normally in cutting chips both hands are moving around and the second both hands are off that larger stack (without any prior verbal declaration), it's all bet. I also want to discourage this in the first place, so I'm really leaning to binding it all just on that basis, he'll be more careful next time.
This all said, I do respect the chips-released standard to absolutely bind a bet. So in circumstances where there's some room for doubt, I reserve the option to tolerate the action and just warn the player.
Also keep in mind your post notes that no verbal declaration was made previously. If the guy had said "I make it 100 k total", then pushed the larger stack out, it's less of a problem, because we know 100k is going to be peeled away. But here we only have the gesture to go by.
Thanks for the great question!
