Mechanism

Normally during inspiration, systolic blood pressure decreases by ≤10 mmHg^[1] and pulse slightly increases. This is because inspiration makes intra-thoracic pressure more negative relative to atmospheric pressure, which increases systemic venous return to the right atrium by reducing pressure on the veins, particularly the venae cavae. However, the decrease in intra-thoracic pressure and stretching of the lungs during inhalation also expands the compliant pulmonary vasculature so that blood pools in the lungs and decreases pulmonary venous return to the left atrium. Also, the increased systemic venous return to the right side of the heart expands the right heart and directly compromises filling of the left side of the heart by slightly bulging the septum to the left, reducing maximum volume. Reduced left-heart filling leads to a reduced stroke volume which manifests as a decrease in systolic blood pressure, leading to a faster heart rate due to the baroreceptor reflex, which stimulates sympathetic outflow to the heart.
Under normal physiologic conditions the large pressure gradient between the right and left ventricles prevents the septum from bulging dramatically into the left ventricle during inspiration. However such bulging does occur during cardiac tamponade where pressure equalizes between all of the chambers of the heart.^[4] Following a zero-sum game principle, as the right ventricle receives more volume it can push the septum into the left ventricle reducing its volume in turn. This additional loss of volume of the left ventricle that only occurs with equalization of the pressures (as in tamponade) allows for the further reduction in volume, so cardiac output is reduced, leading to a further decline in BP. However, in situations where the left ventricular pressure remains higher than the pericardial sac (most frequently from coexisting disease with an elevated left ventricular diastolic pressure), there is no pulsus paradoxus.^[5]
Although one or both of these mechanisms may occur, a third may additionally contribute. The large negative intra-thoracic pressure increases the pressure across the wall of the left ventricle (increased transmural pressure, equivalent to [pressure within ventricle] - [pressure outside of ventricle]). This pressure gradient, resisting the contraction of the left ventricle, causes an increase in afterload. This results in a decrease in stroke volume, contributing to the decreased pulse pressure and increased heart rate as described above.
Pulsus paradoxus occurs not only with severe cardiac tamponade, but also with asthma, obstructive sleep apnea and croup. The mechanism, at least with severe tamponade, is likely very similar to those of hypertrophic and restrictive cardiomyopathies (diastolic dysfunction), where a decrease in Left Ventricular (LV) filling corresponds to an increasingly reduced stroke volume. In other words, with these cardiomyopathies, as LV filling decreases, ejection fraction decreases directly, yet non-linearly and with a negative concavity (negative first and second derivatives). Similarly with tamponade, the degree of diastolic dysfunction is inversely proportional to the LV end-diastolic volume. So during inspiration, since LV filling is lesser relative to that during expiration, the diastolic dysfunction is also proportionally greater, so the systolic pressure drops >10 mmHg. This mechanism is also likely with pericarditis, where diastolic function is chastened.

Pulsus Paradoxus = Systolic BP drops during inspiration