How do you handle listening to the other person if he/she is upset while setting boundaries to avoid dealing with hurtful language?

Try to set boundaries and ground rules in a context that is on neutral ground; not during a conflict or tense time. If you are in a tense moment, be direct, honest, and use the 3 strikes rule--3rd time...end the conversation and suggest picking it up when you've calmed down a bit.

Tell him/her directly that you are uncomfortable with it and that boundaries should be set if not then be there for another session and time where she/he is already calm. And if it all methods fail refer him/her to someone who has more training when it comes to dealing with these kind of cases. To top it all just offer the best of your empathy and compassion, that sums up all the best that you can ever give to that person.

Try and take your mind away from whats happening around you, calm yourself by focusing on someone you love or something happy until you feel better and that you can continue the conversation

I would be a little more stern with them, letting them know that I am only here to support them, and only out for their best interest.

I think it can help to avoid using accusations and tit-for-tat as well as using the to prefix any sentence "I feel..." in stead of "You make me...", "You are...". Just state what you want and stay calm, patient and repetitive. Refuse to get pulled off track, acknowledge how your the person is feeling but always come back to your same boundary. Using phrases like "I understand where you're coming from, but this is what all I can offer", "I can see you're [angry/upset/whatever emotion] but this is all I am willing to compromise on" can help prevent escalation and allow you to return to reaffirming your boundary. You may need to consider taking a time out if the conversation isn't getting anywhere. Just stay strong, refuse to let guilt or anger weaken your stance and stay calm. Eventually the other person will get it!

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I try to take what they are going through into consideration. Also, I am not easily offended by harsh language. Trying to put myself into their shoes also helps :)

Try to understand that they are in a state where everything seems to be irritating. Least we can do is to listen and relate to them.

Trying to relate to the situation and letting them know that everything will be okay, letting them know they aren't alone

I take a moment to process everything they are talking about and stay in a positive mindset and try to help them.