How long does it take before zoloft leaves your blood stream??

Depends on how long you've been taking it and at what dosage. With most non-extended release medications, you're only talking about a few days at most, however, the effects on neurotransmiter levels can last a month or longer... Why do you ask?

Sertraline has half-life of about 26 hr. It means, that it may take about 5-6 days to clear out of the system:
Sertraline (Zoloft) Facts (http://www.emedexpert.com/facts/sertraline-facts.shtml)