What is the meaning of the last phrase here? 但上涨的部分又被不断上涨的成本抵消
Let's go through this part piece by piece.

压力主要体现在皮鞋出口数量与金额上 = The pressure is mainly seen in the number and price of exports. 

曾有数据统计显示 = Statistics have shown clearly that

维持反倾销税的一段时间内，中国对欧盟的鞋类出口增幅明显下降 = after maintaining the anti-dumping law for some time, the growth rate of China's shoe exports has a noticeable decline. 

单价却显著上升 = However, the price of the shoes kept increasing.

So up till now, we have one part that is increasing (the shoe price) and one part that is decreasing (the growth rate of the shoe exports).

Now let's look at final part:

There are 2 nouns phrases that we need to figure out.
上涨的部分 = The part that is growing. As we noted above, this is the price of the shoe.

不断上涨的成本 = The ever increasing costs of making/exporting the shoe.

Then it becomes:

但 [上涨的部分] 又被 [不断上涨的成本] 抵消

抵消 means "canceled out" and "又被" means "have been" and 但 means "but."

Then putting all this together it means:
Yet, the growing price is being canceled out by the rising costs of making/exporting the shoes.