毕业(bì yè) - to graduate, graduation in Mandarin

毕业 (bì yè) is to graduate, and it doubles as the noun graduation in 毕业典礼 (the graduation ceremony), 毕业生 (a graduate) and 毕业证书 (a diploma).

Grammatically it is a verb-object compound: 毕 is the verb, 业 is its object. That means the two halves can be prised apart, which is why 毕了业 and 毕业两年了 are both fine, and why 毕业 can never take another object of its own.

The trap follows straight from that. You cannot say 毕业大学. The school goes in front with 从 (从大学毕业) or behind with the formal 于 (毕业于北京大学). English lets graduate swallow its university directly; Chinese does not.