Note in the sticky at the top of this forum that requests that you post the current Oracle wording of any card in question.
http://www.themanadrain.com/index.php?topic=27205.0Clockspinning:
Buyback 3 (You may pay an additional 3 as you play this spell. If you do, put this card into your hand as it resolves.)
Choose a counter on target permanent or suspended card. Remove that counter from that permanent or card or put another of those counters on it.
Serrated Arrows:
Serrated Arrows comes into play with three arrowhead counters on it.
At the beginning of your upkeep, if there are no arrowhead counters on Serrated Arrows, sacrifice it.
Tap, Remove an arrowhead counter from Serrated Arrows: Put a -1/-1 counter on target creature.
The Oracle text says it pretty well. Look at the colon ( : ) in Serrated Arrows - to the left of any colon is a cost and to the right of the colon is the effect. In this case, if you tap Serrated Arrows AND remove one counter from Serrated Arrows, you get to put a -1/-1 counter on target creature.
In order for Clockspinning to work in this manner, Serrated Arrows would need to be worded with a triggered ability. For example:
Tap: remove a counter from Serrated Arrows.
When a counter is removed from Serrated Arrows, put a -1/-1 counter on target creature.
So, to answer the question briefly, no, Clockspinning will not cause another instance of Serrated Arrow's effect. It can, however, keep Serrated Arrows supplied with counters so that it can be used turn after turn.