This question really has a lot of answers depending on who you ask.  There will be many people that look to the technical aspects of the phone.  Does it emit radiation?  Does it emit radio waves that could be harmful to you?

While many studies have been done trying to enforce or dispute those questions, I don't think any of them have been that conclusive.  

It used to be believed that talking on your cell phone while pumping gas could ignite the fumes and cause an explosion or a fire.  In that case then yes, your cellphone could kill you, although I don't believe any instance of that happening has ever been proven.

If someone were texting and talking on the phone and driving and became distracted, that could be a situation where one might say the cell phone killed that person.

Finally, if you were to talk to the relatives of some of the people who died because they fell off a cliff while trying to take a selfie, they might indicate that yes your cell phone could kill you.  Others might argue it was the poor judgement on their part that caused the accident, but that is a more philosophical debate.

Personally, I think if there were significant dangers to using cell phones we would see much more evidence of it given the proliferation of them.