No, natural selection does not cause mutations and mutations don't cause natural selection.
Evolution is the big picture...a process of species changing over time.
Natural selection is what determines what individuals will survive to pass their genes to the next generation...it doesn't matter if they have mutations or not. If there is something in the environment that affects survival, whichever individuals already have the traits that allow them to survive will survive. If they do not already have those traits, they die...they cannot acquire new traits as a response to that environmental pressure. If none of the species has any trait that will allow them to survive a particular environment, the entire species may go extinct (think of how endangered the Giant Panda is because there is not enough genetic variation for them to survive in the habitat that is changing around them...they can only survive well in their ever-shrinking habitat...when that habitat is gone, they will be gone). If every member of the species has a trait that allows them to survive the environment, then there is no selection among individuals and they all survive.
Let's take a hypothetical example. You have a species that has an enzyme critical for cell function/survival. An individual is born with a mutation in the gene for that enzyme that changes a single amino acid. It's not in a very important part of the enzyme, and it still functions as it needs to function. Over time, that individual has 10 offspring that each have 10 offspring that each have 10 offspring, etc...and the number of individuals in the population that carry that mutation increases. They are never a huge percentage of the population, but steadily increasing. Maybe 5% end up with that mutation. Over centuries, the climate is warming up too. This enzyme, as is common for enzymes, has an optimal temperature range for functioning. At some point in time, the environmental temperature exceeds the optimal range for the enzyme...except for the mutated one...for some reason, that mutation makes it more stable at a slightly higher temperature. 95% of the population with the "original" form of the enzyme start to die off when the temperature gets too high. 5% with the "mutant" form, which by then is just considered a normal variation, survive. That's natural selection. That the mutation happened at some point was not predetermined. If it hadn't happened, 100% of the members of that species would have died when the temperature got too high for the original enzyme to function.
Now, you have a dramatic shift in the population genetics. Instead of 5% of the population having that mutated form of the enzyme, 100% have it (remember, all the others without that form died).
This is quite different from the common misunderstanding where people think 100% of the population had the original form of the enzyme, and when the temperature increased, somehow the gene was made to change to adapt to the new temperature. That's not what happens. The variation has to be there for natural selection to select anything.
Does that make it clearer?