Sure you can sell it that way. It could be structured in a number of ways--such as a wrap mortgage. Or a contract for deed.
However, recognize that you'll be violating the "due on sale" clause in your mortgage. The "due on sale" clause says, essentially, that if you sell or transfer ownership of the property, or any part of it, then the lender can call the loan due and payable immediately. Theoretically, that's a problem; the lender could foreclose. Practically, in today's market, almost no lender is going to care so long as it receives the monthly payments. It's a risk--a very small one today--but one you should be aware of.
Would a bank give you a mortgage on another property? Simple answer: No. Better answer: Possibly not. The reason is that you'd still be responsible for the mortgage on the first property. You haven't gotten rid of it. So the lender is going to consider your total debt and your total monthly obligations. Yes, you're receiving money from the buyer but--similar to renting a place out--a lender won't give you full credit for the amount you're taking in. And you're in a weaker position--you still owe on the mortgage on the first house, but you've transferred ownership in it. Now, if you have enough income, you can do it. To be sure, check with a lender or mortgage broker.
Again, check with a lender . . . and a lawyer . . . for more information.
Hope that helps.