Dictionary
sit-up
from the dictionary:
Pronunciation: (sit up\')
—v.
an exercise movement in which a person lies flat on the back, lifts the torso to a sitting position, and then lies flat again without changing the position of the legs: formerly done with the legs straight but now usually done with the knees bent.
Also, this phrase is used when a person is already sitting but, say, he/she is slouching instead like many kids do in the classrooms nowadays. The teacher would then say \" Sit up, Cameron ! I can\'t see your face !\"
In this example we are also taking about the body movement from the waist up.
conclusion: you \"sit up\" from a lying position or from a sitting position.