That's right.
Actually, it isn't just that your body and mind "think" everything is normal. As far as the reference frame of your ship is concerned, everything really is normal.
And here's the really weird part: You would expect that the astronaut will preceive the earth clocks as going fast, right? But in reality, the exact opposite happens. As far as the astronauts are concerned, it is the earth who is in motion. And since clocks in motion are slowed down, they will preceive the earth's clocks as being slow. Yet, at the same time, we preceive their clocks as going slow relative to us!
So, what's going on here? Isn't this a paradox? No, because comparing earth time and ship time can only be done indirectly, due to the great distance between the earth and the ship.
Perhaps an example will help clear things up:
Let us assume that the ship is launched from earth at 60% the speed of light. The ship is launched at Noon. Four hours later, at 4 PM, we want to compare the clocks on the ship with the clocks on earth.
How do we do that? By sending the following question via radio waves:
"It's 4 PM here. Please respond with the time shown by your clocks the minute you get this message."
Of-course, since the ship is going at 60% the speed of light, it will take the radio signal some time to reach the ship. 6 hours, to be precise. For after 6 hours, at 10 PM, the ship will be 0.60x10=6 light-hours away from earth.
It would take another 6 hours for the astronaut's response to reach the earth. After a total of 12 hours, at 4 AM the following day, the response would reach mission control: "Our clocks read 8 PM".
So far so good. There is no paradox. Both the astronauts and the people left on earth agree about the sequence of events: The earth's clocks showed 4 PM when the meessage was sent. The ship's clocks showed 8 PM when the message was received. The only thing left to do, is to calculate how many hours elapsed between these two events.
We already know that from the earth's point of view, it took 6 hours for the signal to reach the ship. But would the astronauts on the ship agree with this statement? Let us do the calculation:
The message was received at 8 PM, which is 8 ship-hours after launch. From the point of view of the ship, the earth is moving away at 60% the speed of light. So after 8 hours, the earth is 0.60x8=4.8 light hours away.
At the same time, the signal from earth is approaching the ship at exactly the speed of light (the speed of light never changes, even when the source is moving). So every hour, the distance between the earth and the radio waves (as measured from the ship) increases by 1+0.6 = 1.6 light hours. Since the signal (and the ship) is now 4.8 light hours from earth, it must have been sent 4.8/1.6 = 3 hours ago.
So from the astronauts' point of view, the delay wasn't 6 hours. It was only 3 hours. And as we shall see immediately, this disagreement is the reason each party believes the clocks of their colleagues are slow:
For the guys at mission control, The question was received 6 hours after it was sent. Since it was sent at 4 PM, they would conclude that the reply was sent at 10 PM (4+6). And since the reply was "the ship's clocks show 8 PM", this means that the ship's clocks are 2 hours (10-8) slow.
For the astronauts, the question was received only 3 hours after it was sent. Since it was received at 8 PM (by their watch), they would conclude that it was sent at 5 PM (8-3). And since the message stated "It's 4 PM on earth", this means that the earth's clocks are 1 (5-4) hour slow.
Both point of views are correct. There is no paradox, because niether party can look at the other party's clock at real time. Indeed, the very meaning of "real time" is different for the two parties.