How do I fill cracks between stone steps and mortar?
First of all, I hope the mortar wasn't concrete. Concrete and mortar, while related, are two different things. Mortar is meant to be softer and give (rather than the brick or stone giving and thereby cracking). 

The proper solution is to re-tuck-point the joint. That means chip/grind out the old mortar and put new mortar back in. 

Alas, mortared steps are a maintenance nightmare and you'll likely be doing this forever at least bi-annually. I eventually caved and tore out our aging brick stairs (meaning half the brick was spalling and flaking, and weeds were in every joint) and replaced them with colored concrete. Not quite as rustic, but a whole lot safer (the old bricks were slick) and maintenance free.