In theory, this could be possible but would take a lot of time to accomplish because you would need to set your screen sizes/breakpoints and then apply those changes to different classes across the entire theme. You would then need to constantly test between mobile & desktop to make sure the changes are only applying to mobile screen sizes.
Because it would take a long time to develop, this isn't something our Support would be able to cover in the 60 minutes free design time that you get when you use a Shopify free theme.
All of that aside, we would discourage making a change like this because Shopify's free themes are responsive, meaning that they adapt to the device that they are being viewed on. This is crucial for a good user experience, and attempting to disconnect the desktop theme from the mobile could prove problematic and complex.
I'd be very interested to hear why it is you'd want to do that in order to see if there's anything else I can recommend or any insight I can offer! I'd also like to know what your product line is, and your brand! Has your store been open long? How are you finding it so far?
I'm happy to answer any other questions you may have! All the best, Hyde.