The server's resources will be allocated by the operating system as required.
I don't think you really want it to devote no RAM or CPU cycles to anything other than processes run by one account. To do so would be very strange (and cause stability problems).
To allocate all resources available to hosting this one application of yours, just don't run anything else from the server. If there aren't any other hosting accounts or services running, no resources will be dedicated to them, and I have no idea why you would put things on a server which you don't want to consume compute resources.
If your application is running slow and nothing else is competing with it for resources, chances are there is something wrong with the application itself, or elsewhere in your environment. For instance, it might be buggy, or it might have a slow connection to its database if it has one (or to the internet). Look at remote resources that are required.
Another thing that can happen in virtual hosting environments is that the VPS provider can underprovision disks such that access is slow. Consider taking a look at
top; if the majority of CPU time is going to
hi (hardware interrupts, which disk access waiting falls under), that is the problem. Also, check
iotop to see if there is excessive disk I/O.