How to break up with a business partner?

I feel that there would be no reason for you to have any doubts what so ever, if you have made numerous attempts to correct the wrongs of your work colleague, be straight to the point and also remind them that you have tried to give them independence along with some constructive criticism to only end up with unsatisfactory results, and make sure that they understand that the decision to let them go was that of a business standpoint and its nothing personal.

You said partner, so it sounds like there is ownership of something here. You haven’t given any clues at all, and there are so many possibilities. Is there property involved, or is the business entirely thinktank? Dividing assets gets sticky, unless you can afford to do a full buy out.
Really, more details are needed.

Just do it like a relationship. Say like, “It’s not you. It’s me. I guess I just wasn’t ready for a partnership, cause it isn’t what I expected.”

Buy him/her out. Prepare the payment before you give them the bad news. Make sure it’s all kosher with your lawyer.

A good partnership agreement will have a process and method by which the partnership may be dissolved (short of death of one of the principals), which should include dissolution for various business reasons, including loss of business, a choice by one of the partners to pursue business that the other partner/s do not want to join, and other reasons, including non-performance by one or more of the partners.

Since you mention that this is a “business” relationship, the expectation is that there is an equity stake to consider on the part of at least one partner. (You can always simply abandon the partnership if you have no equity to withdraw or don’t mind sacrificing it. In that case you must still take care to disassociate yourself legally from the partnership so that it doesn’t continue to operate in your name, which could involve you in debt and other legal issues – including liability, which could be practically unlimited – without even your awareness.)

One fair way to settle equity is to prepare a buy-out offer for your partner, and then offer it “either way”. That is, your partner can buy you out for the amount that you’ve named, or you could buy him out, and you’d be happy either way. That is an indication that it’s a fair offer; it’s as if you have “cut the cake and offered him first choice of the pieces”. If you are only prepared to buy out your partner at an amount that you name, that’s a tip off that it’s not a very equitable offer. Be prepared for a long, contentious settlement negotiation in that case.

If there is an ongoing “project”, as you mentioned in the question, then you’ll also need to find a way to satisfy any business clients, who may have contracted with the partnership for some object. You’ll need to either produce the completed project before dissolution, find an acceptable alternative that will satisfy the customer, or at the very least return to the customer the full value of money already paid for performance. You don’t want to sour your relationships with customers! (That’s predicated on the assumption that the business ceases to exist. If you plan to buy out your partner and still satisfy the customer, then that may be a moot point.)

Keep in mind for future reference that business partnerships are among the most difficult to maintain, because either partner can expose the other to unlimited personal liability. That’s pretty scary.