"阻挠议事的议员" can be translated into English as "a senator (or member of parliament) who obstructs/filibusters legislative proceedings" or more concisely as "a legislative obstructer/filibusterer" (though the latter is less common in formal contexts and more descriptive).
In more formal or parliamentary-specific language:
"A senator (or MP) engaging in obstructionist tactics during legislative proceedings"
"A member who uses filibustering to delay or block legislative business"
For simplicity and common usage, "a senator/MP who obstructs parliamentary proceedings" works well.
Example:
The opposition party accused several senators of being "obstructers of parliamentary progress" for their delay tactics.
(反对党指责几名参议员使用拖延战术，称他们为“议会进程的阻挠者”。)
Or more directly:
The filibustering senator was criticized for stalling legislative work.
(那位采取阻挠议事策略的参议员因拖延立法工作而受到批评。)