Yes, you have to drop old column and add a new one.

ALTER TABLE dbo.MyTable

DROP COLUMN OldComputedColumn

ALTER TABLE dbo.MyTable

ADD NewComputedColumn AS OtherColumn + 10

In case you weren't yet aware, you can get SSMS to write queries for you. Use the UI to set up the change you want to make, but before you click the Save button (or close the Design window), right click on the design surface and select "Generate Change Script". It will give you a script that you can cut and paste into a query window. It doesn't always give you the most efficient script or even the most efficient method for performing the task, but it will get you started. And it's a good way to get more familiar with (or refresh your memory of) DDL syntax.