What to do when expecting a negative recommendation letter?

A bad review from your present advisor will probably hurt you significantly. However, I think you will do more damage if you try to discredit your advisor's reference ahead of time: you risk sounding like a poor employee, particularly if your advisor is respected in your field.

Instead, I would prepare evidence to counter a possible negative recommendation. If you expect your advisor may critique your productivity, emphasize work you have completed in your interview. Unfortunately, if you have failed to publish your work in your current position, that may be difficult to prove, and the responsibility for that is not only on your advisor but on you as well.

If you anticipate critiques of your work ethic, how well you play with others, etc, and your other reference has not yet submitted a letter, you could ask them to specifically highlight those qualities. If they already submitted a letter, hopefully they already addressed these issues.

I would be careful about how you describe your relationship with your current advisor in the interview: keep the high ground, and don't make judgments of value. If you produced one good publication where your current advisor expected two, don't say "Bob had ridiculous expectations for my productivity" - instead, try something closer to "I worked on two projects with Bob - we were able to publish project 1 after ___ months but ran into setbacks on project 2."

An interview is never the place to bring negativity into the discussion. Always, have nothing but positive things to say about all your committee members. Even if you were treated unfairly by this person, anything negative you say only makes you look bad. Include him in the references...he is/was your advisor. If he gives a negative response to those who inquire about you from him, then that reflects on him, not you. By all means, take the high road, it will show your personality and professionalism in a positive light.

I would ask your current supervisor if you can expect a good reference letter or if you should look for another reference in the future. Perhaps it would give you the opportunity to talk about his negativity towards you and to find an amiable way to continue to collaborate. And it would let you justify to him or discuss frankly his expectations and yours and try to come to an understanding.

If he is going to give you a negative reference, which he probably won't do because, in that case, he should've said he would not write a reference for you, then you can prepare your game plan.