No, you can not restart the game with the same character. There are a couple editors that would let you re-create a high level character, though.

iZakaroN's SaveEditor (or from Kiya's site, with description)

DAD's item editor


Alternately, there is a cheat that would let a low level character get a headstart with gold and potions, etc.

To duplicate items which can be stacked;
Drag a stack out of (or into) your inventory (or container) and hold down the control key before dropping. This will bring up the split stack pane; type in a negative number and hit enter (the checkmark will be greyed out). This can also be done in the trade window.