I took that scene as Crouch wanting to prove to Dumbledore that Voldemort is back, by showing his Dark Mark burning on his arm, which hadn't happened since Voldermort had disappeared all those years ago.
He knew that Harry was being taken to give blood to contribute to the resurrection, and was effectively backing up his claim to Dumbledore that the plot had succeeded by getting Harry to show where he wad been cut for the blood (which Dumbledore could have been expected to know would be a part of such a resurrection ritual).
Getting Dumbledore to verify that Harry had indeed lost blood, combined with the Dark Mark burning simply serves to reinforce the truth Barty is telling, that Voldemort is back, in case Dumbledore might have disregarded the rantings of a clearly crazy person, or not believed what Harry had to say on the matter. The wizarding community is shown to have a slight unwillingness to believe stuff they don't like the sound of.
TL;DR Barty's trying to provide evidence to show Dumbles beyond a shadow of a doubt that Voldemort has returned.