In anger Vs With anger

"In anger" is normal in modern speech to mean "angrily". Using "with anger" sounds archaic, though it may be truncated from something like "with anger in his heart".

The construction "Death rises up with anger" is not usual, so a hearer would need to interpret it. It may mean "angrily", but the word "with" also suggests other possible interpretations. It may mean that anger also rises up alongside Death. It may mean that Death is holding or wearing anger (perhaps to use as a weapon or armour).

The whole extract sounds poetic or dramatic in nature, and all the above meanings, with others, can be overlaid in the mind of an audience.