We propose a unified and deterministic scheme to generate arbitrary single-photon multimode $W$ states in circuit QED. A three-level system (qutrit) is driven by a pump-laser pulse and coupled to $N$ spatially separated resonators. The coupling strength for each spatial mode $g_i$ totally decide the generated single-photon N-mode $W$ state $vert W_N rangle=frac{1}{A}sum_{i=1}^N g_i|0_1 0_2 cdots 1_i 0_{i+1}cdots 0_Nrangle$, so arbitrary $vert W_N rangle$ can be generated just by tuning $g_i$. We could not only generate $W$ states inside resonators but also release them into transmission lines on demand. The time and fidelity for generating (or emitting) $vert W_N rangle$ can both be the same for arbitrary $N$. Remarkably, $vert W_Nrangle$ can be emitted with probability reaching $98.9%$ in $20-50$ ns depending on parameters, comparable to the recently reported fastest two-qubit gate ($30-45$ ns). Finally, the time evolution process is convenient to control since only the pump pulse is time-dependent.
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