Here's my idea for how I'd have liked to have seen the cutter used:
Indy's RPG blows up a truck near the cutter: a bit of wreckage from which kills the driver of the cutter. The cutter then goes out of control (shades of LC tank, admittedly!) and veers right into the jungle and disappears. The chase pretty much goes as in the film except that you could have, say, Indy's duck chasing Spalko's jeep with her possessing the skull, when suddenly the cutter appears from the right directly in front of Spalko. She hits the brakes so as to not be torn up by the driverless machine as it passes in front of her but Indy overtakes her, spins his duck around the front of her jeep, grabbing the skull as he goes, and then tears off down the new path the cutter has made. She could then head back down the path she's already driven down, knowing that the paths should meet again.
So all through the chase, as well as the occupants all switching vehicles and the skull hopping between all of them you could have an out of control cutter occasionally appearing and getting both parties into trouble. Plus it would mean that they could essentially be driving down paths not knowing where they go or what they link up with.
Then, instead of Mutt getting caught in the vines and being left behind: it's Indy. He's left dangling 20ft in the air as the vines snap him upwards, but he turns and sees the cutter heading straight for him! He pulls out a penknife and starts sawing through the vines as quickly as possible, and at the last minute he swings free out of the way of the blades! The return of the swing then lands him on the deck of the cutter: he moves up to the cabin and gives himself one of those Indy-can't-believe-his-own-luck half smiles! Cut to the cliff face where Marion, Mutt et al are being pushed to the edge by Spalko's jeep, when suddenly Indy comes tearing through the treeline in the cutter! He grinds up Spalko's jeep which jams the blades (after making raspberry jam of a couple of commies of course!): the Russians advance on Indy and a fight breaks out on the moving cutter with Mutt hopping aboard to give support- Marion's duck escapes.
Eventually the cutter runs down a steep slope and gets caught in some trees: the crash sending Indy, Mutt and the Russians flying and the mangled jeep into the ants nest. Dovchenko and Indy battle it out, their fight having to hop between various bit of high ground to avoid the ants, when finally the only bit of ground left available to them is under the spinning blades of the cutter, still caught on the slope in the trees by its back wheels! They swing it out some more as the cutter's weight brings it slowly down towards them- they try and force each other's faces into the blades etc. But then Indy is knocked down; he's lying on a log and Dovenchenko is holding him there as the blades are directly above him. Indy manages to kick free and rolls along the log just in time: the log is torn up by the cutter and the half Indy is lying on gets caught on the blade: pulled up around the blade into the air. Indy hangs from the log and lands a kick to Dovenchenko's face just before he is thrown into the air with the log by the force of the spinning blade! Dovenchenko is sent flying back into the other blade: his hand is torn off and he staggers, screaming, into the ants. They then envelop him and drag him away to his death. Indy lands with a thump out of the way of the ants. He sees them swarming towards him however and looks around frantically for a way escape to no avail: just then Ox appears and unveils the skull; using its powers to divert them. They turn around and see the cutter getting covered in ants and dragged down underneath the ground into their nest.