From a driving dynamics point of view, there aren't any immediate concerns that lead me to think it won't work at all. However, that said, nobody has much experience driving vehicles at any fast speeds on the Moon or Mars. The Curiosity rover travels at a maximum of 1.5 meters per minute and the Lunar Roving Vehicle hit top speeds of 13 kilometers per hour. That's not that fast. To get a better idea of max speeds when crossing sand here on Earth, I looked at some cars and vehicles that are specifically designed to race across sand. Most notably, I found the type of vehicle called a "Sandrail" which is specifically designed to race across sandy surfaces and dunes. Here is a video of some of them racing in a competition and as you can see, they get close to taking off despite being in Earth's gravity. These vehicles are pretty close to the cybertruck's acceleration and reach speeds just a bit under paved road max on smooth sand on Earth.
From a pure driving persepective, I don't think the cybertruck would be a good Mars-vehicle as it is because:
- Although it has a high clearance for commercially sold vehicles, it has nowhere near the clearance that's exhibited in the high-speed sandrail vehicles.
- From the looks of the videos, many sandrail vehicles have wheel deflection ranges of over a meter. While I don't know specifically how much the Tesla has, has to be less than 40 cm.
- The Cybertruck's wheels are truck-sized but not optimized for sand. Sandrail vehicles have "paddle" type wheels with big ridges that let them grab onto a lot of sand. This also prevents them from sinking into the sand. Rovers have gotten stuck on Mars after sinking into soft sand and the Cybertruck, especially with the double battery pack, is going to be very heavy. It might not even fare to well on regular Earth sand and quickly dig it's wheels in before going anywhere
- There's a reason that rovers typically have six wheels and have the rocker-bogie wheel suspension system. Traditional car-like suspensions and wheel arrangements are designed for roads and not dusty, sandy, and rocky plains.
Still, driving-dynamics are only the smaller half of the problem (IMO). Most of the problems that would result in trying to drive a Cybertruck on Mars are engineering related:
Cybertruck is not presumably not completely sealed against abrasive dust or the harsh conditions that would be encountered on Mars. I'd expect big electromagnetic motors and bearings to get gunked up rather quickly, especially if you're driving around at high speeds
Tesla's battery technology is not currently equipped to deal with the enormous temperature swings that would be encountered on Mars and the vehicles is presumably not insulated enough to keep the passengers from freezing to death.
Rubber wheels or pressurized wheels like those on almost all cars here on Earth are an absolute non-starter for the low pressure, low temperature Martian surface.
The Cybertruck is not pressurized and does not have any suit-ports or airlocks. Sealing the Cybertruck and pressurizing it would be very difficult as angular shapes with large planes are very difficult to construct strong enough that they don't simply burst. The large, flat windows that give the Cybertruck it's iconic look would need to be ludicrously thick and strong to withstand an atmosphere of pressure pumped in from the inside.
Cybertruck, while large for a street-legal vehicle isn't that big. With two astronauts wearing suits, life support systems, experiments, and equipment it would be extremely cramped; if it's possible to fit all this stuff in the first place. Although this is just speculation, there is probably a minimum size that it makes sense to build a pressurized vehicle and it's probably around the size of a small RV. Vehicles the size of a pickup, like the Cybertruck, will probably still be used but won't have pressurized cabins similar to the Lunar Roving Vehicle.
Many more technical issues that would probably result in it being easier to design a new vehicle almost from the ground up rather than adapting the Cybertruck for Mars usage.
Still, despite the many problems that make the Cybertruck ill-suited for Mars, it still does have some advantages that will probably be carried over into actual Mars exploration vehicles:
Electrically powered. It's unlikely that we'll find oil on Mars and running an internal combustion engine on a planet with basically no atmosphere or fuel doesn't make sense. Mars vehicles will likely have a battery pack and be driven through electrical motors (like all Mars rovers to date)
An "Armored hull". Mars vehicles will be very tough and resilient. They're going to need to withstand all sorts of conditions, and breaking or being breached could result in the rapid death of all occupants. Strength of the pressure vessel will be a priority
A simple "flatpack" design. Transporting something that's boxy and angular or large sheets of metal that need to be folded and assembled on site is much easier than traditional vehicle chassis manufacturing. Straight edges and flat planes also make repairs and replacement parts easy. If metal is procured locally on Mars, transforming it into sheets will be the first step and then folding those sheets into a vehicle, origami-style, will be far easier than traditional multi-stage stamping and shaping processes found in the auto industry today.
