如果这是一个完整的句子,那么不可以省略be动词,因为这个句子缺少谓语动词（do ,did ,does三种语态）,The homework is given by their English teacher.才是正确的
而be doing,to do,done三种时态叫做非谓语动词
省略be动词,实际上是把这个【句子】,变成了一个【名词】
【The homework given by their English teacher】后面一定还接有别的话
比如【The homework given by their English teacher】is too much,而【is】就变成了这句话的谓语动词 ↑ 相当于名词,作主语 ↑