$category = Mage::getModel('catalog/category')->load(176);
    $productCollection = $category->getProductCollection();
    foreach($productCollection as $p){

        Mage::getSingleton('catalog/category_api')
                ->removeProduct(176,$p->getId());
    }

$category = Mage::getModel('catalog/category')->load(176);
$category->setPostedProducts(array());
$category->save();