Joan Rivers -- Endoscopy Clinic Targeted with Death Threats

The clinic where Joan Rivers was undergoing a throat procedure last week is under fire, because fans are blaming the staff for her death ... and are making it clear they're out for blood.

Sources connected to the Yorkville Endoscopy clinic in NYC tell us death threats have been coming in droves since Joan was rushed to the hospital last week. Some of the threats have included -- "If Joan dies, so will you," ... and ... "I hope you people die, you killed an icon."

We're told the clinic has been shutting down early on some days to send employees home -- and additional security's been hired.

As we previously reported ... the NY Health Dept is already reviewing the clinic to see if a full scale investigation is warranted.

10:00 AM PT -- A rep for Yorkville Endoscopy tells us extra security has been hired due to media and cameras outside the facility, claiming, "Security is only to ensure patient safety and privacy."