Your question is as such completely unrelated to your title. However, that it seems related to the body of your question to you is at the heart of your misconception. One simply moves at $1$ second per second through time. It is a meaningless thing to ask how fast one moves through time, so it is true that it is not the case that the faster you move through space, the slower you move through time but it's not because you instead move faster through time. It's a meaningless assertion either way.
What you want to ask is whether a clock $A$, as seen by a given observer $O$, ticks at a slower or faster rate than their own clock $B$ when clock $A$ is moving faster or slower w.r.t. the said observer $O$. Now, this is a meaningful question. Given the correction to your calculation indicated in the other answers, the answer to this meaningful question is that a clock $A$ ticks at a slower rate, as observed by $O$, the faster it moves w.r.t. $O$.
However, it is crucial to understand that this does not mean that "time slows down" for clock $A$. That is, in fact, the central tenet of special relativity -- that all inertial observers observe the same physics. So, nothing unusual happens to $A$ from its own reference frame. That is the very axiom on the basis of which we derive the implication (via coupling it to the existence of a finite invariant speed) that when viewed from the reference frame of $B$, $A$ must appear to have slowed down.