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All you need is the single instruction vqmovun.s16 , vqmovun_s16 in intrinsics.

Vector Saturating(q) Move Unsigned Narrow

int16x8_t input;
uint8x8_t result;
result = vqmovun_s16(input);
Any negative element will be replaced with 0 while all the numbers bigger than 255 will be set as 255 then narrowed to unsigned 8bit elements, and all these in a single cycle, EXACTLY what you need.
There is also vqmovn_s16 which keeps the values signed (-128~127)
PS: Are you working on YUV to RGB conversion? That's the one time I needed this instruction.
int16x8_t q_result;
int16x8_t max_value = vdupq_n_s16(255);
int16x8_t min_value = vdupq_n_s16(0);
uint16x8_t max_mask, min_mask;
max_mask = vcgtq_s16(q_result, max_value);
min_mask = vcltq_s16(q_result, min_value);
q_result = vbslq_s16(max_mask, max_value, q_result);
q_result = vbslq_s16(min_mask, min_value, q_result);
const int16x8_t max_value = vdupq_n_s16(255);
const int16x8_t min_value = vdupq_n_s16(0);
int16x8_t q_result = ...;
q_result = vmaxq_s16(min_value, q_result);
q_result = vminq_s16(max_value, q_result);
        
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