In rare cases it's possible for a baby to choke on it's spit up but very rare and unlikely.
The baby has a natural reflex that coughs up the spit up and the baby will continue coughing the spit up out until their airway clears.
If your baby is coughing on their spit up you should pick the baby up and allow them to sit upright or on your shoulder and pat them on the back to help them get the spit up out.
When laying on their backs the baby may have a harder time of getting the spit up out of their lungs so putting the baby upright can help the baby stop coughing on the spit up.
Most times though the baby will spit up and may cough a little bit and then be just fine.
Babies usually spit up after feeding on formula or breast milk when their stomachs get too full and the excess is spit up or also known as vomit.