There are a number of ways to describe a person who refutes claims or makes assertions without presenting a valid argument, but I don't know of a single word to describe such a person. Examples of people employing tactics similar to those which you've described generally fall within the realm of logical fallacies. Logical fallacies are arguments which might appear at face value to have merit, but actually have no merit, due to the fact that they employ bad logic or faulty assumptions.
Some examples of popularly employed logical fallacies include:
argumentum ad hominem - a personal attack on the person making an argument rather than attacking the argument itself. For example, if someone stated "Crime is on the rise", and someone responded with "No, it's not, because you're a stupid face!", that would qualify as argumentum ad homimem.
argumentum ad temperantiam - also known as "argument to moderation" - an argument which presumes (fallaciously) that the truth can always be found in compromising between two opposite positions.
appeal to ridicule - an attack which presents an opponent's argument as absurd without presenting any evidence to refute it. This is not to be confused with reductio ad absurdum which is a legitimate form of argument.
In your case, the person replying "You are so wrong, it's funny!" appears to be employing appeal to ridicule in place of a legitimate argument.
Please note, however, that bringing this to their attention is unlikely to convince them to present a real argument, and will likely provoke a series of ad hominem attacks.