Survey deletion is possible, but as a dangerous operation is made available only to server administrators. When a survey is deleted all data collected as part of that survey is irretrievably and irreversibly lost. Hence the same steps should be applied as described in actions after the end of the survey.
Make sure you backup your data before deleting a survey! Even if this was training, pre-test, or a field test. In some cases even data collected as part of such exercises can be invaluable for improving the questionnaire, estimating the performance of interviewers, or duration of the survey.
There is rarely any need to delete a survey. Deleting a questionnaire template will delete the whole survey with all data associated with it. In most cases a new server instance should be requested to allow the installation of the most recent version of the Survey Solutions server components.