The short answer is no, you cannot use your mouse in Jupiter Hell. Due to the style and genre of the game, it goes back to very traditional routes where you have to use the arrow keys to move around (if playing on the keyboard).
You cannot use the mouse at all, not even during the menus. Everything is controlled with only the keyboard. There is full controller support, so if it feels strange to use a keyboard, especially the arrow keys, plug in a controller and use that to play the title.
However, if using a controller, you cannot use the left analog stick to move. That can only be done using the D-Pad. The left stick is used in the game for mechanics, but you cannot move with it.
Jupiter Hell uses a grid-based system, but without the use of the mouse to select a path you want to follow. You have to manually hit every movement, based on your inputs, which is only the four cardinal directs, left, right, up, and down. No moving diagonally in Jupiter Hell!
Check out some of ProGameGuides other articles on Jupiter Hell!
