You don't need to reload entire scene. You can reload just one node (and its children). This is the best thing about Godot. Each scene is like a node. So you can create a Scene (say Main.tscn) and have a top level Node (say Main). Attach the timer to your Main node. And the rest of the game scene can be child of the Main node, let's call it 'Game'. So whenever the character dies, you just reload the 'Game' node. And the timer being part of parent node (Main), will continue to tick.
In order to reload a node, I guess you have to call removechild, and then addchild on the parent node.