For kernels compiled without CONFIG_SMP, and without CONFIG_PREEMPT spinlocks do not exist at all. This is an excellent design decision: when no-one else can run at the same time, there is no reason to have a lock.
If the kernel is compiled without CONFIG_SMP, but CONFIG_PREEMPT is set, then spinlocks simply disable preemption, which is sufficient to prevent any races. For most purposes, we can think of preemption as equivalent to SMP, and not worry about it separately.
You should always test your locking code with CONFIG_SMP and CONFIG_PREEMPT enabled, even if you don't have an SMP test box, because it will still catch some kinds of locking bugs.
Mutexes still exist, because they are required for synchronization between user contexts, as we will see below.