No. SpiderOak never removes content from your backup without you explicitly requesting it. If you delete something from your computer, SpiderOak will move its copy of the item to the Deleted Items bin display within that device in the Manage tab. Deleted items stay in the bin perpetually -- until you decide to intentionally remove them.
Many backup services only store deleted items for a short period of weeks or months, and if you do not realize the need to recover that file within this time frame, the backup file will be lost. SpiderOak prefers to take an all-inclusive approach.