This phrase is used metaphorically to describe overcommitting, not literally chewing. Getting into three sports at once, she's bitten off more than she can chew.
Pro Tip 2/3
Negative Connotation
It suggests a negative outcome from taking on too much. He bit off more than he could chew and missed all his project deadlines.
Pro Tip 3/3
Use with Caution
Avoid using this phrase in formal or professional contexts as it can seem informal. In the meeting, I didn't say he'd bitten off more than he could chew.