For a simple graph \( G \) with the vertex set \( V \) and the edge set \( E \), a labeling \( \lambda: V \cup E \to \{1, 2, 3, \ldots, k\} \) is called a vertex-irregular total \( k \)-labeling of \( G \) if for any two different vertices \( x \) and \( y \) in \( V \) we have \( wt(x) \neq wt(y) \), where \( wt(x) = \lambda(x) + \sum_{xy \in E} \lambda(xy) \).
The total vertex-irregular strength, denoted by \( tvs(G) \), is the smallest positive integer \( k \) for which \( G \) has a vertex-irregular total \( k \)-labeling. In this paper, we determine the total vertex-irregular strength of a disjoint union of \( t \) copies of a path, denoted by \( tP_n \). We prove that for any \( t \geq 2 \),
\[
tvs(tP_n) =
\begin{cases}
t & \text{for } n = 1, \\
t+1 & \text{for } 2 \leq n \leq 3, \\
\lceil \frac{nt+1}{3} \rceil & \text{for } n \geq 4.
\end{cases}
\]