Atmega128 improper reset
You have given very scant information, so specific comments are not possible.  Here are some general things to look at:

Make sure the microcontroller and all other chips are properly bypassed.  There should be a 1 &micro;F or so ceramic cap physcially close to each part across the power and ground pins.  If you haven't done this, all else is pointless.

Look carefully at your ground.  Ideally you have a ground plane under all the low power circuitry.  This can be connected in at most one place to external ground if you want to.  Make sure that the motor current, including its ground return currents, don't flow near the low power section.

Look at the 3.3 V line with a scope right at the micro.  Set the trigger to falling edge, and a little lower voltage than what it actually is, like maybe 3.1 V.  If the scope triggers when the motor shuts off, then you messed up the separation of the ground and/or power between the low and high power sections.

Consider that there may not be a electrical problem at all.  You may have a firmware bug that causes strange things to happen when the motor is shut off.  Replace the motor with a resistor that draws significantly less than the motor.  If it still happens, then a power glitch from the motor shutting off is unlikely the cause.

Your FET gate drive makes no sense.  I can't even guess what you think a emitter follower does for you.  What it actually does is reduce the maximum gate voltage by about 600 mV.  The emitter follower gives you current gain, but there is no point to that since a few &micro;s longer turning on the FET seems irrelevant from your description.

Make sure the FET can work with the low gate voltage you are giving it, and the 24 V it has to withstand when off.  You should be using a FET rated for at least 30 V D-S, and specified with sufficiently low Rdson at a bit below 3.3 V gate drive.  This assumes you fix the gate drive circuit first.

Make sure the reverse diode across the relay coil is functioning and really connected.