You would be violating Same-Origin Policy since SharePoint does not expose services through CORS or JSONP.
You would have to use another approach, such as proxy, auto hosted app or sandboxed solution (deprecated).
If you want to manipulate a list (or web-part) using JS, you can use the JSLink Feature to do that:
1) Simply go to Site Contents of the site that includes the web-part you want to handle with JS and open the Site Assets Library. Upload you JS file there (.js).
2) Then go to the site and Edit it and find the web-part/list of interest. On the upper right side of the web-part click the arrow for the drop-down menu and select Edit Web Part.
3) Now a menu poped up on the right, with Miscellaneous appearing on ist bottom. Expand Miscellaneous and on the JS Link Option enter:
In case you have a question on the JS syntax to retrieve data from the list and handle it, comment and I can edit this answer to include a sample and explaination.