Caso MySQL/Se/Então

Acho que você quer dizer que se o stock > 1000 então outra cor 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..

mas se você realmente quer dizer isso,

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..

Mais uma coisa, você também precisa usar GROUP BY cláusula ou então você estará retornando apenas um registro mesmo que tenha 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