The mechanism by which CO2 mitigates hiccups is by stimulating the sympathetic nervous system to keep the airways more open.
CO2 is a chemical indicator of our bodies expending energy. A large increase of this tells our cells there is a large environmental challenge we are facing, which reinforces sympathetic activation. If you were running from a bear, your survival chances increase if your cells use the biproducts of activation to further increase activation in a positive feedback loop. If instead CO2 was a parasympathetic stimulus your body in essence would be hitting the gas and brakes at the same time, which would make you less effective in emergencies and also lead to syndromes of autonomic dysfunction.
Breathing supraphysiological doses of CO2 (eg 3 to 7% CO2 gas mixtures) has been found to induce panic attacks in people, even those without an amygdala (!), and can actually be used to reduce anxiety by way of training increased physiological tolerance to normal levels of CO2, which is lacking in people who have breathing pattern disorders which lean towards hyperventilation and sympathetic activation.
In a sentence, CO2 is a stressor, and in the practice of breathing exercises it acts as a hormetic eustress.
