I'm not aware of a db that is operating normally without a log.
first of all, delete command is logged. If you look for non-logged operations, please check BOL for "bulk insert", "select into", "truncate table" etc. They will not cause the log to grow.
But a lot of times, you have to use "DELETE". you can turn the database into simple recovery mode 'cause it is testing server. The log will be truncated.
You can also run scheduled job to do "backup log xx with truncate_only" with proper frequency.
When none of the above works, you need to look into if you have open transactions by DBCC OPENTRAN. You should also modify your delete statement to do transactions at a smaller scale, say, commit transaction every 100 rows. It will allow the log to be checkpointed and truncated.
In the database properties window navigate to Transaction Log tab and see how much is allocated. I suspect that 602 is the number you're going to see. You'll probably need to do shrinkfile against your trx log. The reason Backup Transaction Log option is disabled is because your database is in Simple Recovery mode.