An electron caused to spin in a magnetic field gives off synchrotronic radiation (Synchrotron radiation (also known as magnetobremsstrahlung radiation) is the electromagnetic radiation emitted when charged particles are accelerated radially, i.e., when they are subject to an acceleration perpendicular to their velocity (a ⊥ v).).
Once out of the magnetic field, does the electron continue to spin or does it resume a straight line after all of the energy provided by the magnetic field dissipates?
First, we need to understand why an electron moves in a circular track (i.e. orbits) under uniform magnetic field. In the classical picture, charges in a magnetic field $B$ experience a force according to the Lorentz force law, $$F=qv\times B.$$
The direction of the magnetic force is always perpendicular to the velocity (as we can see from the cross product). So the Lorentz force provides a radial acceleration, which explains why the electron orbits (i.e. the electron performs circular motion for unifrom magnetic field).
When an electron exit from an area with magnetic field, it will no longer experience the Lorentz force, and (if there are no other forces acting on it) it will move in a straight line (from Newton's 1st law).
The spin of the electron is irrelevant to the trajectory of the electron.
