Urination and defecation are obviously going to take place over a space of two or three days on the cross. I avoided defecation in
The Serpent's Eye by having Sabina imprisoned for a couple of days on a liquid diet before her crucifixion. Here's where it was mentioned:
As I brushed past him, he said, “What’s in that basket? No more food for her, just water and broth. Don’t want her shitting and making a stinking mess when we hammer the nails in tomorrow.”
And pissing from the cross is mentioned several times in that story:
“And pissing from the cross, girl, the last thing you want to do is anything else that’s uncomfortable, so never try to hold it. You’ll do it sooner or later, so make it easy on yourself and forget about the crowd. Just don’t make the mistake of pissing on a guard or executioner; they can and will make you pay for that.
Another mention:
"Keep them well watered. A farting mule never gets tired, and a pissing slave won’t die soon. I want to come back tomorrow and find this slave girl going up and down as often as a whore’s skirts.”
Another mention:
I pulled her upper lip back, pressed my thumb against her gums and took it away, then counted heartbeats as I watched the pink color return, just like checking a sick mule. Three heartbeats was a little longer than I liked. The smell of her piss was strong, too. She was losing water faster than she was drinking it. If she didn’t get more she would weaken and die too quickly.
Sabina, talking about having to piss after the guard had whipped her between her legs:
And then I had to pee, and my urine felt like scalding water where it dribbled out, bringing tears to my eyes.
Sometimes, I have a girl who's about to be crucified ask if she can pee first. Sometimes she gets to, and sometimes she doesn't. Here's such a case from Damian's Roman Crucifictions:
When the soldiers gripped Antonia’s arms and began dragging her toward her cross, she moaned in terror but did not beg. Just as they were about to force her down on the ground, her terrified eyes fastened on Carinus and she appealed to him, sobbing, “Wait! P-please, sir, c-could you just let me pee first? P-please sir, I-I’ll be quick. It’s all I ask, I don’t want to, to lose control…”
The soldiers hesitated, but Carinus’ reply was quick and decisive. “No, you may not. And if you piss on any of us when the nails go in, I can promise you that we will make you regret that. You are about to die the worst of deaths as Roman law requires, but I can make it even worse than that.” Carinus hated anything that disrupted the continuity of his crucifixions, and he had heard all kinds of last-second pleas like this. Justice should be as harsh and unyielding as the timber of the cross.
And here's one from Faithful Sayings where they let her pee first:
Jennifer is no match for the two men, and they quickly pull her hands loose, seize her by the arms and drag her toward the cross that waits for her. Defeated, she sobs in despair. She continues to beg, but now she only has one thing left that might delay her crucifixion, if only for a moment. “Please, please, in the name of God, let me pee! Please, before you put me on the cross!” she sobs.
Mohammed does not speak English, but he knows a few words and he understands what she means. He speaks to Adel and they stop dragging her for a moment. Mohammed points to the ground at Jennifer’s feet, looking her in the face, and says “dalee”. She knows a few words of Pashto. “Dalee” and “huree”, “here” and “there”, are two of them. Jennifer understands that he means for her to squat and urinate on the ground where she stands.
The two men continue to hold Jennifer’s arms as she spreads her feet and lowers herself to squat between them. Thousands of Afghanis in the stadium watch and laugh as her stream of urine splatters on the bare ground between her feet, growing into a small dark puddle that slowly soaks into the brown dust. Her humiliation at being forced to do this very private, basic thing like an animal in front of so many is crushing. Her own stench revolts her. She stares at a point on the ground between her knees to avoid meeting the eyes of the men watching her. She has no idea yet that the Al-Jazeera cameras, of which there are several in the stadium, are transmitting her shame to billions.
Jennifer purposely holds back to make these few seconds that her execution is delayed last as long as possible. Inevitably, her stream of urine slows to a trickle, and then as the last few golden drops are falling, Mohammed and Adel pull her to her feet.
In a story I'm working on now, I used urination by the victim as part of the story - it got her into trouble. This is the way the story starts out:
It was when Verres the carnifex was kneeling beneath Arria’s cross driving the last of the big square nails through her feet that she lost control of her bladder. She didn’t realize it at the time, because her consciousness, her very being, was completely overwhelmed with the agony of being crucified.
But Verres did.
And it didn’t matter to him that she was writhing in excruciating pain when it happened, screaming helplessly, heart pounding and on the edge of slipping into a faint, and thus unaware of what she had done.
As surely as night followed day, she would pay for that.
And I've written many times of urine splattering on the ground when the condemned pissed while crucified. It's a humiliating, public thing that's part of the torture of the cross.