Remove elements from deep nested list
If you want to target lists like {1., 1812.}, and the level at which they occur can vary, I would use Replace with a negative level:
Replace[list, {_, b__} :> {b}, {-2}]
{{{1812.}, {4262.}, {1272.}, {4048.}, {3961.}, {7739.}, {3173.}, {1201.}, {6856.}, {11860.}, {1324.}, {3457.}, {5038.}, {18731.}, {4624.}, {6527.}, {4971.}, {4936.}, {2371.}, {3750.}, {5660.}, {2451.}, {6293.}, {4577.}, {2005.}, {1428.}, {6300.}, {1145.}, {2797.}, {3096.}, {3249.}, {2323.}, {4063.}, {3751.}, {4430.}, {2228.}, {2141.}, {881.87}, {6139.}, {5055.}, {1821.}, {64625.}, {6462.}, {3415.}, {5792.}, {2384.}, {2193.}, {2934.}, {5664.}, {10404.}, {3382.}, {3105.}, {7323.}, {9947.}, {6282.}, {7470.}, {18522.}, {3243.}, {2813.}, {5574.}, {2719.}, {7508.}, {3832.}, {5858.}, {4174.}, {10320.}, {3402.}, {10592.}}, {{1154.}, {2259.}, {650.77}, {1210.}, {1812.}, {2630.}, {1373.}, {1028.}, {2351.}, {2614.}, {1494.}, {1480.}, {1903.}, {2058.}, {2520.}, {3663.}, {2352.}, {1950.}, {1125.}, {1991.}, {2718.}, {1447.}, {3137.}, {2014.}, {1040.}, {735.41}, {3531.}, {597.25}, {1181.}, {2203.}, {1837.}, {1217.}, {1793.}, {2520.}, {1972.}, {1021.}, {1317.}, {428.54}, {3340.}, {2294.}, {1125.}, {2758.}, {2510.}, {1500.}, {2800.}, {1284.}, {1854.}, {1567.}, {3042.}, {3823.}, {1852.}, {1550.}, {4062.}, {5808.}, {2971.}, {3837.}, {6249.}, {3008.}, {1604.}, {2172.}, {1424.}, {2998.}, {3669.}, {2870.}, {2313.}, {5777.}, {1945.}, {6480.}}}
To remove the 1's specifically:
Something like this uses ReplaceAll to replace all the 1.'s with the Nothing element:
lis = (*your data*)
lis /. (1. -> Nothing)
To remove the first element of each sublist at the 2nd level:
In case you case you aren't necessarily using 1.'s, but want to replace just replace the first part of each deeply nested sublist, consider something like Replace with a level spec:
lis = (*your data*)
Replace[lis, ({x_, y__} :> {y}), {2}]
Alternatively:
lis = (*your data*)
Map[Rest, lis, {2}]
list[[All, All, 2;;]] (* or *)
Drop[list, None, None, 1]
{{{1812.}, {4262.}, {1272.}, {4048.}, {3961.}, {7739.}, {3173.}, {1201.}, {6856.}, {11860.}, {1324.}, {3457.}, {5038.}, {18731.}, {4624.}, {6527.}, {4971.}, {4936.}, {2371.}, {3750.}, {5660.}, {2451.}, {6293.}, {4577.}, {2005.}, {1428.}, {6300.}, {1145.}, {2797.}, {3096.}, {3249.}, {2323.}, {4063.}, {3751.}, {4430.}, {2228.}, {2141.}, {881.87}, {6139.}, {5055.}, {1821.}, {64625.}, {6462.}, {3415.}, {5792.}, {2384.}, {2193.}, {2934.}, {5664.}, {10404.}, {3382.}, {3105.}, {7323.}, {9947.}, {6282.}, {7470.}, {18522.}, {3243.}, {2813.}, {5574.}, {2719.}, {7508.}, {3832.}, {5858.}, {4174.}, {10320.}, {3402.}, {10592.}}, {{1154.}, {2259.}, {650.77}, {1210.}, {1812.}, {2630.}, {1373.}, {1028.}, {2351.}, {2614.}, {1494.}, {1480.}, {1903.}, {2058.}, {2520.}, {3663.}, {2352.}, {1950.}, {1125.}, {1991.}, {2718.}, {1447.}, {3137.}, {2014.}, {1040.}, {735.41}, {3531.}, {597.25}, {1181.}, {2203.}, {1837.}, {1217.}, {1793.}, {2520.}, {1972.}, {1021.}, {1317.}, {428.54}, {3340.}, {2294.}, {1125.}, {2758.}, {2510.}, {1500.}, {2800.}, {1284.}, {1854.}, {1567.}, {3042.}, {3823.}, {1852.}, {1550.}, {4062.}, {5808.}, {2971.}, {3837.}, {6249.}, {3008.}, {1604.}, {2172.}, {1424.}, {2998.}, {3669.}, {2870.}, {2313.}, {5777.}, {1945.}, {6480.}}}
{Dimensions @ %, Dimensions[list]}
{{2, 68, 1}, {2, 68, 2}}
SeedRandom[1]
lst = RandomReal[100, {100, 1000, 9}];
(res0 = lst[[All,All,2;;]])//RepeatedTiming// First
0.0022
(res1 = Drop[lst, None, None, 1];) // RepeatedTiming // First
0.0034
(res2 = Map[Rest, lst, {2}];) // RepeatedTiming // First
0.023
(res3 = Replace[lst, ({x_, y__} :> {y}), {2}];) // RepeatedTiming // First
0.139
res0 = res1 == res2 == res3
True