In order to improve the energy dissipation effect of the connection components of steel truss joints and optimize the arrangement of the components, a new replaceable component railway pier structure was proposed, referring to the transmission tower structure. The new pier consists of four pier columns and the steel truss connection system between the columns. Based on the OpenSees platform, a dynamic analysis model of the new railway pier was established. 56 seismic records were input, and incremental dynamic analysis (IDA) was carried out to investigate the damage evolution law of the connection components and the influence of component yielding on the stress of the rebar in the middle and bottom of the pier. The results show that the steel truss connection system yields in a row and consumes energy in a graded manner. The yielding order of the second and third rows of the steel truss connection system is always in the forefront. The second and third rows are the main energy-consuming rows, followed by the fourth, fifth, and sixth rows, and finally the seventh, eighth, and first rows, with the first and eighth rows being less likely to yield. The outer chord members in each row yield first, followed by the inner chord members, and the vertical and diagonal members are less likely to yield. The yielding of the pier columns occurs after the yielding of the chord members of the steel truss. The yielding of the outer chord members in the steel truss connection system has a certain inhibitory effect on the stress increase of the rebar in the pier columns and at the bottom of the pier, and the inhibitory effect on the bottom of the pier is better than that in the middle.