Hello,

if you are getting caught by the UR3e or any other model of Universal Robots. How can you release the Brakes or free yourself? Is there any safety button or function for this?

Best wishes 
Dieter

Just push back on the robot, you can force it out of the way by slipping the clutches.  That is how it is designed to free yourself from entrapment.  I have never been forced to do that with it being stuck on my body, but up against a machine several times

The robot is also designed to back off 10mm from where the protective stop happened so to avoid the need to move the robot manually.