The specific negative effects of biotechnology depends on what type of biotechnology you're referring to. However, there are some general negatives that apply to many different types of biotechnology.
In order to test and improve biotechnology, organisms must be modified. This can include testing on animals and plants, which can deteriorate quality of life for these organisms. Testing on animals in particular doesn't go through animal rights supporters well (for obvious reasons). So, biotechnology can pose an ethical threat to nature.
Also, there's a possibility of genetically modified organisms and traits spreading to other organisms that are similar. For example, in 1999, there was a controversy over genetically modified crops that contained proteins that eliminate the need for dusting them to get rid of pests. This protein travelled over to other similar crops and killed some beneficial organisms that ate them, even though the protein didn't harm humans. People continue to oppose the use of GMO foods, claiming that they are unhealthy and continue to affect the environment. Possible environmental threats are another example of a negative of biotechnology.
Lastly, there is the general state of biotechnology being understudied. In many cases, the outcome of biotechnology tests are unknown and success has varied in tests throughout the years. This creates a list of additional unknown possibilities (including negatives) of the testing that people tend not to like.
In short, biotechnology can pose ethical and environmental threats and the results of current testing can lead to further negatives that are unknown due to understudying.
