Oven heating element just blew (WOW!). Went & killed the breaker. Clock on range is still running. And is flipping me off
That is a very common fault for a heating element.
Check and see if the stove top works, the fault may not have tripped the breaker.
Most older homes have a 40 amp circuit double pole for a range and 50 amp is becoming more popular. (If in another part of the world a different size breaker is possible)  A 120v oven doubtful 120v GFCI very doubtful with older wiring.
If the fault tripped the breaker it is safe. If the fault did not trip the breaker don’t use the oven and it should be fine until it can be repaired by you if you own the oven/range or by the land lord.
Appliance repair is not covered by the NEC the premises wiring is.
If it can be unplugged and it would make you feel better unplug it if plugged in. I always unplug or verify the power is off prior to replacing these elements (a very simple job).
If the clock is on the oven/ range it most likely did not trip the breaker.
Edit added post element repair:
With the original post stating the clock was on but not mentioning it had a strange reading I did not think to mention that when the element blew it may have fried the controller.
The high current short in some cases vaporizes the traces on the control board some cases just the oven won’t work in others the metal slag from the event shorts out the controls.
With the damage to the board a new board may be needed. It has been a while but the control board can usually be found on line.
I think they come in white and black but that could be a different brand. The relays that turn on the elements are on the board so when there is a short from the element failure the traces turn into the fuses.
Search for your model # and you may find one under 50 but they range up to 150 range actual prices are off topic because they are always changing.