Contractor cut wire in wall - all still works fine - is this dangerous?
Does this all sound right and I should just not worry about it?


If it is causing you concern, you could pay another electrician for a second opinion. I wouldn't bother but you may feel it worthwhile.


  do I need to start tearing down walls to figure out where the cut wire came from?


If you must know where the wire leads to, that might eventually be necessary. 

There are other tools that can be used for tracing wires without requiring opening up the walls - for example, tone-generators are often used on telecom wiring, I imagine you could isolate the power supply to the house and use that kind of tool. 

This might be a lot of work for little reward. 

A disconnected wire is unlikely to pose a hazard unless it is a ground/earth wire which might mean that some light-fitting or power outlet which shoudl be earthed is not. An electrician can test lights etc to test the earthing arrangements meet code. You can buy relatively inexpensive tools to test outlets - these might give you some reassurance.



If the electrician has pronounced it safe and has capped off the wire, I would leave it at that unless you have good reason to mistrust the electrician.