code: public void delete(String path)
          throws DbxException
      {
          DbxPathV1.checkArgNonRoot("path", path);
  
          String[] params = {
              "root", "auto",
              "path", path,
          };
  
          doPost(host.getApi(), "1/fileops/delete", params, null, new DbxRequestUtil.ResponseHandler<Void>() {
              @Override
              public Void handle(HttpRequestor.Response response)
                  throws DbxException
              {
                  if (response.getStatusCode() != 200) throw DbxRequestUtil.unexpectedStatus(response);
                  return null;
              }
          });
      }
docs: Delete a file or folder from Dropbox.