Note that the following commands have not been tested, but based off of other ones so should work.
Open a terminal and run the following two commands to delete level.dat and level.dat_old
rm ~/.minecraft/saves/Demo_World/level.dat rm ~/.minecraft/saves/Demo_World/level.dat_old
Should be able to open up Minecraft and have the timer reset. Note that all the achievments in the game will be reset as well.