When I create a new incident from the ticketing application, I want to remove start date. Is this possible?

Yes, you can do that. See Drake's instructions below to find out how, 

You can actually use internal ticketing forms to manage which standard fields appear when filling out a new ticket. Internal forms give you the power to select which fields appear and even make some fields required. Keep in mind that some fields like Title, Priority, and Status are not configurable as they are required by all tickets.

Internal forms are found in Admin -> Tickets -> Internal Forms. You can create a separate form for each ticket classification (incident, problem, change, release) and these forms will be applied - once they are enabled - to all new tickets of these classifications created from the Ticketing application going forward.