Note: Deleting all of your issues may not be the best choice. Read about other options here.
With bulk actions - both deleting and resolving - you can only do up to 1000 issues at a time. When in your issue dashboard for a given project you can select issues matching a given query,
is:unresolved for example, and then select Resolve or use the dropdown to Delete Issues:
Should you wish to use the API you can use the Bulk Mutate endpoint or Bulk Remove endpoint for resolving and deleting, respectively.