Trading in iPhone

From what I understand you are wanting to trade in your iPhone and are asking if taking out SIM card will remove the service. If this is your question then yes taking out a SIM card in a phone removes the service. Also, to your other question your iPhone does need to be fully payed for to trade it in.

The trade in instructions will tell you what to do, and one step is removing your SIM card.

You can then use the SIM card in a new phone or may destroy it, depending on your carrier's policies.

Did you buy it from your carrier or from Apple directly?

Then it's just up to whatever terms your carrier has when it comes to iPhone trade-in. Also, why do you want to take out the SIM card?