Can I use both of Grindclock's abilities at the same time?
When a card has 2 separate sets of "cost: effect", these are 2 separate abilities. You can choose to activate either the first ability or the second ability. Because the cost of both abilities is "tap", you will not normally be able to activate both in the same turn.

If you do untap the card using another spell or ability, then yes, you can use Grindclock's same ability again in the same turn.