Before we know why one of the builder's hands got cut off, we need to go back and ask a few questions about the conversation between Prince Narvok and The mayor.
First of all, why Prince Narvok doesn't have any problems after the talk with The mayor, and second of all how does The mayor plan to protect his townspeople if he just accepts the words of Prince Narvok?
The first question has already been answered, The mayor just accepted all of Prince Narvok's orders, but the second question is a little bit tricky, as The mayor played a mind game to His Highness by saying
"Oh, Your Highness, please forgive this lowly peasant"
Prince Narvok then replied
"Speak"
After having permission to speak, The mayor set his plan into action by stating
"This lowly peasant has a suggestion,"
The Prince then curious and ask
"Oh? What is it? If you don't satisfy me with your suggestion, you'll live without a head,"
The mayor then bowed to The Prince with fearfulness in his body, but secretly, he smirked a little bit, after that he said
"Of course, Your Highness,"
Followed by the plan
"As Your Highness already knew, those "high rankers" will use every opportunity to stop Your Highness's works,"
Then Prince replied with curiosity
"Which is?"
The mayor replied shortly
"Which is this, the troop's preparation"
Prince Narvok asked
"How exactly?"
The mayor answered
"If Your Highness just let us out without any troops seeing it, they'll become curious, eventually they'll start to fabricate the story for fun,"
Then one of The guards put his sword on The mayor's throat instantly and said
"Are you just belittling the Royale guards right now?"
The mayor replied with a smile and trembling at the same time
"Of course not sir, but we have to prepare for the worst, for His Highness's sake"
The guard heard that and shouted
"YOU!"
But got stopped by Prince Narvok's hand, Prince Narvok asked the follow-up question
"What do you suggest then?"
The mayor explains
"All His Highness have to do is let us stay for a little while before we leave the town for His Highness's generosity, seen by everyone, and order the troops to protect us from danger as His Highness's grateful consideration for the lowly people like us,"
The Prince then asked with a glare
"Are you telling me to order my troops to protect you? As the lowly peasants?"
Every guard in the room starts to point their sword at The mayor immediately, The mayor then answers back
"Of course not Your Highness, this lowly peasant just wants the troops to treat us a little better, we will do all the charity for them in return, from giving them food, finding them a comfortable place to stay to helping them with small things, Your Highness"
After listening to the suggestion Prince Narvok laughed and said
"YOU'RE AMAZING, HAHAHAHA.
Alright, you got my word, and you better keep yours"
The mayor replied with a smile on his face, plus his eyes closed
"With my head on the line, Your Highness,"
And that's the reason why The builder's hand flew off, The Troops helped them because they were charity people in the guard's eyes, plus the order of The Prince could be used as an excuse to interfere The builder and the town people conflict, but there's 1 suspicious point that doesn't make sense, why did The builders have lust toward the girl but The Troops doesn't? Because the people, of course, they intentionally make that 1 girl beautiful and the other not so much, to seduce those Builders, The Troops on the other hand only have a treatment like they're family, for example, sob story and gentle words with very good but simple foods to make them feel like they belong in there, that's the reason why we get to this situation.