How to use TypeScript to map a large object to a smaller interface?

Typescript types do not have a runtime impact and so casting an object to different types will have no tangible effect on that object at runtime.

One of the goals of TypesScript:

9. Use a consistent, fully erasable, structural type system.

emphasis added by me

If you want to modify an object you need code beyond types to perform the modification. Given the inability to convert between values and types like you are looking for (see this issue for further discussion), you will need to do something like:

export interface SmallerInterface {
    ipsa: number[];
    elit: any[];
}

export const smallerKeys = ['ipsa', 'elit'];

// Later once you have a result
const result = await makeRequest();
const reducedResult = smallerKeys.reduce((obj, key) =>
    ({ 
        ...obj, 
        [key]: result[key],
    }),
    {}
) as SmallerInterface;