MySQL Caso/Si/Entonces

Supongo que quiere decir que si el stock > 1000 luego otro color not green .

SELECT  Beer.Beer, 
        Beer.Brewery, 
        Beer.Style, 
        Beer.ABV, 
        Beer.Hops, 
        Beer.SRM,
        Sum(BeerStock.Quantity) totalQuantity,
        CASE WHEN Sum(BeerStock.Quantity) < 0 THEN ''
            WHEN Sum(BeerStock.Quantity) BETWEEN 0 AND 999 THEN 'Red'
            WHEN Sum(BeerStock.Quantity) BETWEEN 1000 AND 4999 THEN 'Yellow'
            WHEN Sum(BeerStock.Quantity) BETWEEN 5000 AND 9999 THEN 'GREEN'
            WHEN Sum(BeerStock.Quantity) >= 10000 THEN 'Another Color' 
        END
FROM    Beer
        INNER JOIN BeerStock
            ON Beer.Beer = BeerStock.Beer
-- Where    ..other conditions..

pero si realmente lo dices en serio,

SELECT  Beer.Beer, 
        Beer.Brewery, 
        Beer.Style, 
        Beer.ABV, 
        Beer.Hops, 
        Beer.SRM,
        Sum(BeerStock.Quantity) totalQuantity,
        CASE WHEN Sum(BeerStock.Quantity) < 0 THEN ''
            WHEN Sum(BeerStock.Quantity) BETWEEN 0 AND 999 THEN 'Red'
            WHEN Sum(BeerStock.Quantity) BETWEEN 1000 AND 4999 THEN 'Yellow'
            WHEN Sum(BeerStock.Quantity) >= 5000 THEN 'GREEN'
        END
FROM    Beer
        INNER JOIN BeerStock
            ON Beer.Beer = BeerStock.Beer
-- Where    ..other conditions..

Una cosa más, también necesita usar GROUP BY cláusula o, de lo contrario, devolverá solo un registro incluso si tiene registros diferentes,

SELECT  Beer.Beer, 
        Beer.Brewery, 
        Beer.Style, 
        Beer.ABV, 
        Beer.Hops, 
        Beer.SRM,
        Sum(BeerStock.Quantity) totalQuantity,
        CASE WHEN Sum(BeerStock.Quantity) < 0 THEN ''
            WHEN Sum(BeerStock.Quantity) BETWEEN 0 AND 999 THEN 'Red'
            WHEN Sum(BeerStock.Quantity) BETWEEN 1000 AND 4999 THEN 'Yellow'
            WHEN Sum(BeerStock.Quantity) BETWEEN 5000 AND 9999 THEN 'GREEN'
            WHEN Sum(BeerStock.Quantity) >= 10000 THEN 'Another Color' 
        END
FROM    Beer
        INNER JOIN BeerStock
            ON Beer.Beer = BeerStock.Beer
-- Where    ..other conditions..
GROUP   BY Beer.Beer, 
        Beer.Brewery, 
        Beer.Style, 
        Beer.ABV, 
        Beer.Hops, 
        Beer.SRM