This is not, of course, a simple issue. Your affiliate marketer goes off and infringes on someone's trademark, steals copyrighted content, spams, or does any assortment of actions that are illegal. Under the CAN-SPAM Act, you may very well be liable for the affiliate's "creative" commercial email program, and will usually be sued as the beneficiary of the misconduct. Typically if you did not conduct due diligence, and had no meaningful monitoring or auditing program in place, you'll have liability. Some states have passed laws that make you absolutely 100% liable.
Other misconduct is more difficult to evaluate in this context. We go back to the old principle of the nature of the relationship: is the affiliate an agent or an independent contractor? This analysis centers upon your control over the vendor. Control, when we consider it in the context of third party misconduct, is defined for the most part as having the ability to direct and control the conduct. Think of the difference as being an employee working for you as opposed to a contractor doing its own thing in an office far away. The former is an agent, the latter is not. However, if you knew, or reasonably should have known, of contractor misconduct, and you did not take reasonable steps to stop it, you will likely have responsibility for the conduct either due to an agency relationship or through theories of conspiracy. The odds are high that if your affiliate is sued then you will be sued, and the cost of defending and winning such a suit should cause you to take steps, in a public way, to only let those with good reputations join your affiliate marketing program, and then to implement performance standards and actively monitor compliance of your vendors. When misconduct occurs, you should consider terminating the relationship, although this is not always an easy decision to make.
If the affiliate is generating significant revenue for you and you value the relationship, there are ways to maintain it. But first determine what effect the improper conduct had on the revenue. If the revenue is in great part a result of the misconduct, discount that revenue from the value equation, and then decide if it is worth investing the time, effort, and resources to maintain the relationship. You'll be wise to seek legal counsel at this point to assist you. You need to be very confident that the affiliate can, and will, change its ways, that a reasonable person will believe that given all of the publicly available facts, and that you are willing to undertake a program of monitoring that will show ongoing vigilance. There are a lot of factors to take into consideration in handing out "second chances".
So, you need to have a due diligence program in place before accepting an affiliate marketer, you need to have performance standards established, you need to have an audit program in place to assure compliance with the standards, and you need to act swiftly when problems arise. Otherwise, you may very well end up on the receiving end of a federal lawsuit, and that is never a pretty picture.