Mixing of oxygenated and deoxygenated blood is somthing which takes place in the animals with two or three chambered heart. There won't be a lot of physiological effects. Just that the blood would become semi-oxygenated and the effeciency of the body would decrease as the amount of oxygen in oxygenated blood would decrease. Moreover haemoglobin has more affinity for CO₂ and this would also effect.
Such cases are also found in mammals when the Foramen Ovale does not close to form fossa ovalis and blood can flow between the right and the left arteries.( They call it :दिल का छेद )
This can lead to suffocation, decreased efficiency of body and in some cases Death.