Other than just walking away, is there a better way to handle this type of negotiation strategy?
Assuming this question is not just a big joke, this exchange is so ridiculous and insulting it's impossible to know whether the HM was being serious.
If he is serious
If he is serious then your attitude should be that you can't consider working for someone who can be so casually insulting.
I mean, ask him how he would like it if, after you were hired, whenever you were asked to provide an estimate of the time required to complete a task, you negotiated like this:
HM: I need you to create features A, B, C, and D.
OP: I can do that in 5 weeks.
HM: Is there any way you can do it sooner than that?
OP: No, I'm going to need 7 weeks.
HM: Can we compromise on 6 weeks...
OP: No, it's 8 weeks.
HM: I give up. 8 weeks then.
OP: But it's only going to have features A, B, and C.
(As @acpilot says, you wouldn't get to do this more than once.)
You do not want someone, who thinks he may do this but you may not, to be in control of your livelihood. This will be especially painful for you since you really like all the other aspects of the job, so you will stick with it until your health and self-esteem are all but totally destroyed before finally saving yourself.
It were much better for you, in the long run, to walk away now.
BUT you specified "Other than just walking away". So don't just walk away. Walk away with style and grace. One really good way to do this is to mimic his actions with your own inverse negotiation until it all breaks down. (Bonus ego points for you if the HM has to be the one to point out that convergence is impossible.)
Now you will have have saved yourself from a destructive situation, and handled yourself well in a very difficult circumstance. You would be amazed at how much better you will feel going into your next negotiation.
If he is just testing you
Perhaps he is throwing this strange negotiation in your face just to see how you will respond. If he is just testing you then you should rise to the occasion and adopt an even more fantastic position. You will have to keep up.
I recommend that you begin to mimic his actions with your own inverse negotiation. Watch carefully for the first signs that the HM realizes that it is up to him to get this runaway conversation under control, and play along with any gambit that seems to lead to a graceful exit.
Eventually you can point out that (as @Carpetsmoker says) this is a childish game that might be funny in a sitcom, but not appropriate in a real-world professional environment. After that you can expect to settle down to a serious real-life negotiation.
In any case, you should negotiate something like this:
HM: "We would be glad to bring you on board with a salary of MR -
OP: "I think based on my experience in the field I think pay of MR +
$2k is appropriate."
HM: "We will revise our offer to MR - $10k."
OP: "Well, I'm willing to come down to MR + $4k."
HM: "Our final offer is MR - $11k."
OP: "I'm sorry, but I can't possibly survive on less than MR + $5k."
Notice that in order to use this approach, you do not have to know how serious the HM actually is. You simply respond in kind until he eventually tells you. (@michi calls this "pacing".)
Your goal is to secure the job, but only in a way that does not set you up for an expensive and excruciating failure. You must stand up to the HM somehow. I think there is no better way to do this than to mirror the HM until he gives up.