I know from reading books on bow making that in order to stop the wood from cracking it needs to be seasoned properly. When you first cut down the tree, coat the ends with Elmer's glue or latex paint to seal them off. Then you need to let the wood sit and dry for a while before you start working it. If you leave the wood in log form, it will take many months or even a couple years to season properly. If you split the log it won't take nearly as long.

Another thing I just thought I think the best approach would be to cut down a whole tree and then split the log, what you will end up with will be pie-slice shaped pieces that you could work down to a rounded shape once they're seasoned. To split the log, chop it at the end with an ax to make it crack along a grain line (preferably in the middle). Then drive stakes into the crack to make it split further until the log is completely split in half (length wise). Repeat the process with each new half until they're the right size for a spear shaft.

Also I think you'll want to cut down a tree that has straight grain. Having straight grain probably isn't as important a with spear shaft as it is with a bow because a spear doesn't have to bend but I think it would make your project easier because then your shafts will be automatically straight. To see if a tree has straight grain, just look at the pattern of the bark. It should run vertically up and down the tree and not twist or bend or anything like that.

Just so you know, I haven't made a spear before, this is just stuff I've read in bow making books or I just thought of, but I hope it helps.