On a quick glimpse, "sagged" and "relaxed" seem similar, but there is a subtle difference in meaning:
"To sag" means to lose the neccesary (internal) support and therefore to succumb to gravity. It's what happens before collapsing. It often has some negative connotation, succesting weakness, age or decay: a sagging plant or a sagging roof. When a person "sags" it's often due to sadness (e.g. having recieved bad news), other examples are bad posture (like sagging shoulders) and fainting.
"To relax" means to loosen excess tension or over-alertness. It has a positive connotation.
For your example "relax" would be the better choice.